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# Here's a question.

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A motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. If the river flows at​ 2mph, find the speed of the boat in still water.

Sep 20, 2017

#1
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A motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. If the river flows at​ 2mph, find the speed of the boat in still water.

Distance  / Rate  = Time

Let the rate of the boat in still water  = R

Against the current the rate of the boat  = R - 2

With the current the rate of the boat  = R + 2

So......equate the time

5 / ( R - 2)   = 7 / ( R + 2)      cross-multiply

5 ( R + 2)   = 7 (R  - 2)     simplify

5R + 10  = 7R - 14      rearrange as

24   =  2R

12  = R    =    12 mph

The time it takes =   5 / [12- 2]  = 5 / 10   = 1/2 hr   Sep 20, 2017
#2
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Ah...thank you!!! Well now I see what was wrong...my equation was this:

5 / (R + 2)  =  7 / (R - 2) hectictar  Sep 20, 2017
#3
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These are sometimes tricky...ones  !!!!   Sep 20, 2017