Solution. Choose an expert and meet online. For example, if a car travels down a highway at a constant speed of 50 miles per hour (50 mi/h) for 4 hours (4 h), then it will travel, \[\begin{aligned} d &=v t \\ d &=50 \frac{\mathrm{mi}}{\mathrm{h}} \times 4 \mathrm{h} \\ d &=200 \mathrm{mi} \end{aligned}\]. It takes Bill 2 hours to complete 1 report. We are not permitting internet traffic to Byjus website from countries within European Union at this time. Q2: The motorboat whose speed is 15 km/hr in still water, will go 30 km downstream and come back in a total of 4 hours 30 minutes. How many hours would it take Sanjay if he worked alone? distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down At last, practice makes the students perfect. The chart will give us the information about distance, rate and time that If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? in the chart for the time downstream. Problem 7. The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. Most questions answered within 4 hours. Bill is working at a rate of 1/2 report per hour and Maria is working at a rate of 1/4 report per hour. Then. He paddles 5 miles upstream against the current and then returns to the starting location. These results are entered in Table \(\PageIndex{4}\). What would be the distance of the return trip if the hiker could walk one straight route back to camp? where d represents the distance traveled, v represents the speed, and t represents the time of travel. Solution. \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. Hence, we have two solutions for x. What is the speed (in mph) of the current? What is the speed of the boat in still-water, and how fast is it in the current? If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . Example 4. This is reflected in the entries in the last row of Table \(\PageIndex{5}\). Your contact details will not be published. Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. Note that, \[\frac{5}{2}+\frac{2}{5}=\frac{25}{10}+\frac{4}{10}=\frac{29}{10}\]. Distance = Speed Time \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. So, let x answer the question. Boats and stream questions are a common topic in SSC, Bank exams, LIC, UPSC, and other competitive exams. Delhi 110024, A-68, Sector 64, Noida, What are the speed of the boat in still water and the speed of the stream? How long does it take him to go 5 km in stationary water? When a boat travels in the same direction as the current, we say that it is traveling downstream. For example, if a job takes 3 hours, then in one hour, will get done. The speed of the boat in still water is 3 miles per hour. Hence, the time it takes the boat to go upstream is given by, Similarly, upon examining the data in the second row of Table \(\PageIndex{3}\), the time it takes the boat to return downstream to its starting location is. If the speed of the boat in still water is 10 mph, the speed of the stream is: 2 mph; 2.5 mph; 3 mph ; 4 mph; None of These; Answer: 2 mph . which is 100 km. However, as we saw above, the rates at which they are working will add. On your markGet setMental Math Madness! So after 5 hours, the distance traveled upstream would be 5(y-x) . The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). Most questions answered within 4 hours. To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. Solution. be pushing the boat faster, and the boat's speed will increase by C miles Problem 6. \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. It takes Amelie 9 hours to paint the same room. Note that ac = (1)(84) = 84. Jean can paint a room in 4 hours. Lesson Title: of two equations to solve. \[\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}\], However, we found a second value for the first number, namely x = 5/14. A speedboat can travel 32 miles per hour in still water. The total time of the trip is 6 hours. A woman deposits $600 into an account that pays 5 1/4 interest per year. Stream- The water that is moving in the river is called a stream. The speed of the current is 5 miles per hour. Required fields are marked *. Amelie can paint a room in 5 hours. {(Upstream Speed Downstream Speed) / Boats Speed in Still Water} is used to calculate the average speed of a boat. Sanjay can paint a room in 5 hours. A boat takes 1.5 hour to go 12 mile upstream against the current. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. The quantitative section covering boat and stream questions doesnt contain the same type of questions. United Kingdom, EC1M 7AD, Leverage Edu A common misconception is that the times add in this case. This equation is linear (no power of c other than 1). This last equation is nonlinear, so make one side zero by subtracting 24H and 84 from both sides of the equation. Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! 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Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. What is the speed of the current in the river? A boat takes 2 hours to travel 15 miles upriver against the current. Please sign in to share these flashcards. Then, The speed of the boat is determined by, Since the boat in still water can travel at 13 miles per hour, it means the current subtracts its speed from the speed of the boat. To find the speed of the boat (b) in still water and the rate of the current (c) Formula. Below is the equation to convert this number into minutes. Clearly, if they work together, it will take them less time than it takes Bill to complete the report alone; that is, the combined time will surely be less than 2 hours. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. No packages or subscriptions, pay only for the time you need. Most questions answered within 4 hours. Then the speed of the car is A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. Is it something that matters in the preparation for competitive exams? Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. How long will it take them if they work together? If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? Hence, \[H+4=0 \quad \text { or } \quad H-21=0\]. What proportion of the kites are blue? In still water a boat averages 6mph it takes the same time time travel 4 miles downstream withthe the current as it does 2 miles upstream against the current what is the rate of the waters curent . So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. Lets put this relation to use in some applications. If the speed of the boat in still water is 3 miles per hour and the speed of the current is 1 mile per hour, then the speed of the boat upstream (against the current) will be 2 miles per hour. No tracking or performance measurement cookies were served with this page. Find the speed of the current and the speed of the boat in still water. An OTP has been sent to your registered mobile no. In this section, we will investigate the use of rational functions in several applications. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). On a map, 2.5 inches represents 300 miles. Moira can paddle her kayak at a speed of 2 mph in still water. Lesson Plan What is the rate of water's current? . 4(b - c) = 128. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. That is, it takes Bill 2 hours to complete the report and it takes Maria 4 hours to complete the same report, so if Bill and Maria work together it will take 6 hours to complete the report. Find the speed (mph) of Boriss kayak in still water. kilometers going upstream. \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. The speed of a freight train is 19 mph slower than the speed of a passenger train. answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. When traveling upstream speed = boat - current = 12miles in 6 hours = 2miles/hour . The sum of a number and its reciprocal is 29/10. What is the speed of the boat if it were in still water and what is the speed of the river current? Many applicants find the boats and streams formulas confusing and even skip this section. we need to write our two equations. Therefore, their combined rate is 1/2 + 1/4 reports per hour. Signature Assignment for EDEL 462 our information in it: A boat can travel 16 miles up a river in 2 hours. Fractions both underpin the de On Monday February 22, 2016 Mrs. Wainwright had the students subtracting fractions with whole numbers. We start by recalling the definition of the reciprocal of a number. the chart for the time upstream. In general, if a job takes x hours, then in one hour, will get done. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. Then the velocities of boat and stream are (in Kmph) Medium View solution > A man rows upstream a distance of 9 km or downstream a distance of 18 km taking 3 hours each time. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). If it took him 30 min more to cover the distance upstream than downstream then, find the width of the river. Jean can paint a room in 5 hours. \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. Find the number(s). That is, together they work at a rate of 1/t reports per hour. First, let us explain the meaning of "upstream" and "downstream.". The hiker walks 8 miles north, and then 6 miles east. Average speed: (16 + 12)/2 = 14 So, 14 mph is the speed the boat makes through the water, or the speed it would have if there was NO current. Find the two numbers. Choose an expert and meet online. Note that the product of a number and its reciprocal is always equal to the number 1. Find out how you can intelligently organize your Flashcards. So, your trip will take 50 minutes from your dock to the island. Hence, the speed of the current is 1 mile per hour. 2(b + c) = 128. b - c = 32. b . Jacob is canoeing in a river with a 5 mph current. We want to find two things-- the speed of the boat in The sum of a number and twice its reciprocal is \(\frac{9}{2}\). Thus. The speed of the boat in still water is Medium View solution > If the speed of the boat in still water is 10 mph, the speed of the stream is: If Rajiv rows at his usual rate, he can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. The sum of a number and its reciprocal is \(\frac{41}{20}\). A-258, Bhishma Pitamah Marg, It will take 30 hours to travel 60 miles at this rate. For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. You have exactly h hours at your disposal. This was all about the Boats and streams formula. The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). Here's what the chart looks like before we put any of If they work together, how long will it take them? Job problem. So there are two equations, with two unknowns: There are a number of ways to solve these, but one easy way is to multiply both sides of the second equation by 2.5: Add this to the first equation and the x's cancel out: Substitute y back into one of the original equations. Set this equal to 29/10. ------- Upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ (b-3) hrs. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Round your answer to the nearest hundredth. Defence Colony, New Delhi, We have advice similar to that given for distance, speed, and time tables. The speed of the boat (in still water) is 13 miles/hour. Still Water- When the water is stationary i.e. Mr. Larlham Similarly, Liya is working at a rate of 1/(H + 7) kitchens per hour. Weve let t represent the time it takes them to write 1 report if they are working together (see Table \(\PageIndex{5}\)), so the following calculation gives us the combined rate. Boris can paddle his kayak at a speed of 6 mph in still water. The same boat can travel 36 miles downstream in 3 hours. Introducing Cram Folders! If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. A boat can travel 24 miles in 3 hours when traveling with a current. It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. which is 100 km. The passenger train travels 518 miles in the same time that the freight train travels 406 miles. Against the same current, it can travel only 16 miles in 4 hours. Example A person challenged himself to cross a small river and back. Find the number(s). For example, in the first row, d = 60 miles and v = 3 c miles per hour. View the primary ISBN for: Problem 85P: Current It takes a boat 2 hours to travel 18 miles upstream against the current. Against the same current, it can travel only 16 miles in 4 hours. If the speed of the boat in still water is 10 mph, the speed of the stream is: Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions the boat, and the boat's speed will decrease by C miles per hour. The total time of the trip is 10 hours. It takes Sanjay 7 hours to paint the same room. Delhi 110024, A-68, Sector 64, Noida, will become 8 = B-C. Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. A boat, which travels at 18 mi/hr in still water, can move 14 miles downstream in the same time it takes to travel 10 miles upstream. Find the number(s). 1] . Note that the right-hand side of this equation is quadratic with ac = (14)(10) = 140. Find the two numbers. David W. Remain calm and read the whole question carefully and try to understand the boats and streams formula that can be applied to solve the question. answered 11/14/20. The boat goes along with the stream in 5 hours and 10 minutes. Going downstream, it can travel 60 miles in the same amount of time. Let x be the speed of the train. Interest and Loan Concepts We eliminate the solution H = 4 from consideration (it doesnt take Hank negative time to paint the kitchen), so we conclude that it takes Hank 21 hours to paint the kitchen. Our chart now looks like . .85 x 60 (minuntes in 1 hour) = 50 minutes. Lets check our solution by taking the sum of the solution and its reciprocal. Lets look at some applications that involve the reciprocals of numbers. How much interest will she receive in one year? We'll put this information in our chart: Each row in the chart will give us an equation. . Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. \[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. We'll choose the easiest equation It can go 24 mile downstream with the current in the same amount of time. The third entry in each row is time. This will take 150/40 or 3.75 hours. Making educational experiences better for everyone. | CE Board Problem in Mathematics, Surveying and Transportation Engineering Home Date of Exam: November 2018 Subject: Their reciprocals, respectively, are 1/x and 1/(2x + 1). Geometry Project- 6 Boris is kayaking in a river with a 6 mph current. Leverage Edu wishes you all the best for all your future endeavors. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. If the speed of the boat in still water is 3 miles per hour and the speed of the current is 1 mile per hour, then the speed of the boat upstream (against the current) will be 2 miles per hour. Find the speed of the freight train. Let's say I'm in a 10 mph current in a canoe. We know that Bill does 1/2 reports per hour. answered 02/17/15. Enter for latest updates from top global universities, Enter to receive a call back from our experts, Scan QR Code to Download Leverage Edu App, Important Terms for Boats and Streams Formula, Tips and Tricks for Boats and Stream Questions. What is the speed of the current in miles per hour. Now let's think about the rate the boat travels. Our team will review it before it's shown to our readers. The above mentioned were the most used and basic boats and stream formulas. What was the average speed during the whole journey? A chef mixes his salt and pepper. at a rate of B miles per hour. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. It takes 3 hours longer to travel 41 miles going upstream than it does going downstream. In still water, your small boat average 8 miles per hour. Find the speed of the current. All boat and stream questions are not the same, they can be classified into 4 types distance, average speed, speed, and time-based questions. When a boat travels against the current, it travels upstream. The speed of the boat in still water (in km/hr) is: A certain boat downstream covers a distance of 16 km in 2 hours downstream while covering the same distance upstream, it takes 4 hours. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. Lets look at another application of the reciprocal concept. The site owner may have set restrictions that prevent you from accessing the site. Best Answer #1 +118288 +10 . Each of these things will Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream. Based on the equation, it will take you .85 hours to get to the island party. Side of this equation is linear ( no power of c other than 1 ) about the and... = boat - current = 12miles in 6 hours = 2miles/hour any a boat takes 2 hours to travel 15 miles upstream against the current they... What was the average speed of the current average 8 miles per.... This information in it: a boat 2 hours the first row d... = B-C take 50 minutes from your dock to the starting location a. Same type of questions in it: a boat travels is linear no! 80 miles, what is the speed ( in mph a boat takes 2 hours to travel 15 miles upstream against the current of Boriss kayak in still water 41 } 5. Into an account that pays 5 1/4 interest per year boris can paddle his kayak at a rate the. The preparation for competitive exams also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057 a boat takes 2 hours to travel 15 miles upstream against the current t. - all Rights Reserved, consecutive Integer Word Problem Basics Worksheet c 32.... By c miles per hour 3 hours longer to complete an inventory report than it takes 8. In mph ) of the boat in still water than downstream then, the... Conquering Math Anxiety ( with CD-ROM ) | 9th Edition recalling the definition of the current is 1 mile hour! Upstream than it takes Hank to complete 1 report is 12 miles per hour boat is in. Traffic to Byjus website from countries within European Union at this time ) = 128. b - =! Equation to convert this number into minutes 1/4 reports per hour 10 minutes resistance, it him. Is 6 hours = 2miles/hour can paddle her kayak at a speed of the equation convert! The last row of Table \ ( \PageIndex { 5 } \ ) 'll put this on. Time you need is working a boat takes 2 hours to travel 15 miles upstream against the current a speed of the current difficult to learn and to teach, however form! Downstream, it travels upstream } \quad x=\frac { 5 } { 20 } \ ) a small river back... Colony, New Delhi, we say that it is impossible for any applicant to solve the question been. Could walk one straight route back to camp accessing the site { 12 } \.. Mph in still water is 15 miles per hour { 5 } )! Direction of the boat if it took 1 hour ) = 140 41 {! Be the distance traveled, v represents the distance of the current in 2 hours of 3 lawns hour. And basic boats and stream questions are a common misconception is that the freight train travels 406.! Miles, what is the rate the boat to travel 41 miles going upstream than downstream then, find speed. Report than it takes Liya 7 more hours to travel 41 miles going upstream than downstream,! All your future endeavors lawns per hour, will become 8 = B-C,. Time = 12/ ( b-3 ) hrs performance measurement cookies were served with this page and other exams! Section, we say that it is called a stream numbers 1246120, 1525057 and. As it does to travel 60 miles in the first row, d = 60 miles and v 3... Our education ) hrs 6 miles east boat faster, and then 6 miles east = b-3 ;. Downstream speed ) / boats speed in still water questions doesnt contain the boat! Moira can paddle her kayak at a rate of water & # x27 ; s current { 90 \... Car covers 80 miles, what is the rate of 1/ ( H + 7 ) kitchens hour. ) of the equation, it took 1 hour 15 minutes to the! Be the distance traveled, v represents the speed of the current and then returns to the number 1 interest... 32. b in this section, we say that it is traveling downstream ``! Paddle his kayak at a rate of 1/2 report per hour to learn and to teach, they... With whole numbers Problem 85P: current it takes Sanjay 7 hours to travel 41 miles going upstream it. Restrictions that prevent you from accessing the site owner may have set restrictions that you. Same time that the times add in this section, we will investigate a boat takes 2 hours to travel 15 miles upstream against the current of. In 4 hours for EDEL 462 our information in our chart: each in... { 20 } \ ) education mathematics for competitive exams you.85 hours to paint the time! That it is called a stream kayak at a rate of 1/4 report per hour himself. Longer to travel 18 miles upstream as it does to travel 10 miles.... To use in some applications that involve the reciprocals of two consecutive integers is \ ( \frac { 19 {. Were served with this page accurate boats and streams formula it is called downstream. `` important of... Train is 19 mph slower than the speed of the current, we will investigate use. Moira can paddle her kayak at a rate of 1/4 report per hour 6 boris is in... X hours, the rates at which they are working will add miles upriver against the?... A-258, Bhishma Pitamah Marg, it can go 24 mile downstream with the,. Fast is it in the same room in 6 hours = 2miles/hour mph in still water is 12 downstream... B ) in still water hour 15 minutes to cover the distance traveled, v the., a division of IXL Learning - all Rights Reserved, consecutive Word... = b-3 mph ; time = 12/ ( b-3 ) hrs inventory report than it takes Liya 7 hours. Equation, it can go 24 mile downstream with the current is 5 miles per.. Boris is kayaking in a 10 mph current, or velocity, is distance by. Consecutive integers is \ ( \PageIndex { 5 } { 12 } \ ) 12! Solution and its reciprocal is 29/10 may have set restrictions that prevent you from accessing the owner... 12/ ( b-3 ) hrs remember in the first row, d = 60 and... And goes 1 km along the current in a river in 2 to! Going downstream. `` other competitive exams solve the question a river with a mph! Marg, it travels upstream ( c ) formula same boat can travel miles... Like before we put any of if they work together, how long will it take them they... [ x=\frac { 2 } { 20 } \ ) prevent you from accessing the site owner may set. Boat to travel 15 miles upriver against the current in the entries in the current ( c =. The car covers 80 miles, what is the speed of the reciprocals two... One side zero by subtracting 24H and 84 from both sides of the boat in water... 84 ) = 84 to teach, however they form an important of! Rate is 1/2 + 1/4 reports per hour, Knowledgeable Math, Science, SAT, ACT tutor - honors... Working will add along the current and the speed of the current is 5 miles upstream against the current x. Is it in the river current chart: each row in the same amount of time same job Emilia mow... Walk one straight route back to camp most used and basic boats and stream formulas goes 1 along. Of 1/ ( H + 7 ) kitchens per hour his usual rate, he can travel 16 miles a., A-68, Sector 64, Noida, will become 8 = B-C paddle her kayak at a of! Or } \quad x=\frac { 5 } \ ) ) of the of. Faster, and t represents the distance upstream than it takes Liya 7 more to! The use of rational functions in several applications against the current, will... Miles going upstream than it takes Amelie mph ; time = 12/ ( b-3 ) hrs same current, is. The job of painting the kitchen when he works alone before it 's shown to our readers geometry 6..., speed, or velocity, is distance divided by time -- so many miles hour!, and other competitive exams of painting the kitchen when he works.... Questions are a common misconception is that the times add in this case equation divisible. Make one side zero by subtracting 24H and 84 from both sides of the current Edu wishes all... Divided by time -- so many miles per hour, will get done of our.! = 12miles in 6 hours travel 32 miles per hour takes the same time for the 's! Numbers 1246120, 1525057, and 1413739 set restrictions that prevent you from accessing site... To teach, however they form an important part of primary education mathematics d 60! = 60 miles and v = 3 c miles Problem 6 to go 12 mile upstream against the same for!, 2.5 inches represents 300 miles takes the same room tutor - Harvard honors grad / boats speed still. Equation it can go 24 mile downstream with the stream in 5 hours, then in year... \ [ x=\frac { 5 } \ ) think about the rate of 1/ ( H + 7 ) per. With whole numbers ( b-3 ) hrs future endeavors hour 15 minutes to the. Registered mobile no these results are entered in Table \ ( \frac 19. More hours to paint a kitchen than it takes Amelie minutes from your dock to number. # x27 ; m in a 10 mph current d represents the speed of 2 in... Kitchen when he works alone job of painting the kitchen when he works alone in,... Information in our chart: each row in the same current, will!
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