SOLUTION: The boat could go 104 miles downstream in the same time it took to go 56 miles upstream. If the speed of the boat was 20 mph in still water, What was the speed of the current?

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Question 147172: The boat could go 104 miles downstream in the same time it took to go 56 miles upstream. If the speed of the boat was 20 mph in still water, What was the speed of the current?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
d=rt Start with the distance-rate-time formula.


104=%2820%2Br%29%2At Plug in d=104 and r=20%2Br. Let's call this equation 1.


104%2F%2820%2Br%29=t Divide both sides by 20%2Br to isolate t


So t=104%2F%2820%2Br%29


d=rt Go back to the distance-rate-time formula


56=%2820-r%29%2At Plug in d=56 and r=20-r. Let's call this equation 2.



56=%2820-r%29%2A%28104%2F%2820%2Br%29%29 Plug in t=104%2F%2820%2Br%29


56%2820%2Br%29=104%2820-r%29 Multiply both sides by 20%2Br


1120%2B56r=2080-104r Distribute.


56r=2080-104r-1120 Subtract 1120 from both sides.


56r%2B104r=2080-1120 Add 104r to both sides.


160r=2080-1120 Combine like terms on the left side.


160r=960 Combine like terms on the right side.


r=%28960%29%2F%28160%29 Divide both sides by 160 to isolate r.


r=6 Reduce.


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Answer:

So the answer is r=6


This means that the speed of the river is 6 mph