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Help 12

 Feb 27, 2018
 #1
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This one is a little difficult, NSS

 

Remember that   Distance /Rate  = Time

 

Let's call his rate in still water, R

 

So.......

 

[Distance] / [ Rate with current] + Distance / [Rate against current ] = Total Time

 

22.5 / [R + 6]  + 22.5 / [ R - 6 ]  =  9

 

Get a common denominator  on the left

 

[ 22.5(R - 6)  + 22.5 (R + 6 ) ]  / [ (R + 6)(R - 6 ) ]  =  9

 

[ 22,5R + 22.5R ] /  [ R^2 - 36]  =  9     multiply both sides by [ R^2 - 36 ]

 

45R  = 9 [R^2 - 36 ]    divide both sides by 9

 

5R  = R^2  - 36      subtract 5R  from both sides

 

R^2 - 5R -  36   = 0     factor

 

(R - 9 ) ( R + 4)  =  0

 

Setting each factor to 0  and solving for r produces

 

R  = 9     or R  = -4

 

But R  is positive

 

So...R  = 9 mph  = his rate in still water [ on the lake ]

 

 

 

cool cool cool

 Feb 27, 2018

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