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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.

hectictar  Sep 20, 2017
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 #1
avatar+79673 
+2

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

 

 

cool cool cool

CPhill  Sep 20, 2017
 #2
avatar+5541 
+1

Ah...thank you!!!  laugh Well now I see what was wrong...my equation was this:

 

5 / (R + 2)  =  7 / (R - 2)      angry

hectictar  Sep 20, 2017
 #3
avatar+79673 
+1

These are sometimes tricky...ones  !!!!

 

 

cool cool cool

CPhill  Sep 20, 2017

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