SOLUTION: A paddle boat can move at a speed of 20km/h in still water. The boat is paddles 10km downstream in a river in the same time it takes to go 5km upstream. What is the speed of the ri

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A paddle boat can move at a speed of 20km/h in still water. The boat is paddles 10km downstream in a river in the same time it takes to go 5km upstream. What is the speed of the ri      Log On


   

Question 994638: A paddle boat can move at a speed of 20km/h in still water. The boat is paddles 10km downstream in a river in the same time it takes to go 5km upstream. What is the speed of the river?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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r=rate of river
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Upstream:
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time%5Bupstream%5D=distance%2Frate
time%5Bupstream%5D=%285km%29%2F%2820kph-r%29
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Downstream:
time%5Bdownstream%5D=distance%2Frate
time%5Bdownstream%5D=10km%2F%2820kph%2Br%29
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Since time%5Bupstream%5D=time%5Bdownstream%5D:
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5km%2F%2820kph-r%29=10km%2F%2820kph%2Br%29
%285km%29%2820kph%2Br%29=%2810km%29%2820kph-r%29
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%28100km%5E2%29_per_hr%2B5r_km=%28200km%5E2%29_per_hr-10r_km
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15r_km=%28100km%5E2%29_per_hr
r=6.667 km/hr
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ANSWER: The speed of the current was 6.667 kilometers per hour.
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CHECK:
time%5Bupstream%5D=time%5Bdownstream%5D
5km%2F%2820kph-6.667kph%29=10km%2F%2820kph%2B6.667kph%29
5km%2F13.333kph=10km%2F20.667kph
0.375hr=0.375hr