+0

# Help 12

0
32
1
+2001

Help 12

NotSoSmart  Feb 27, 2018
Sort:

#1
+83946
+1

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 ]

CPhill  Feb 27, 2018

### 12 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details