+128408 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 ]
Help 12
