#1**+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