A canoe travels on a river whose current is running at 6 miles per hour. After traveling 175 miles upstream, the canoe turns around and makes the 175 -mile trip back downstream. The trip up and back takes 10 hours. What is the speed of the canoe in still water?

The speed going up stream is x - 6

The speed going downstream is x + 6

SO to find how long you take going upstream is 175 / (x - 6)

Downstream is 175 / (x + 6)

Add those 2 fractions together and get a total of 10

175 / (x - 6) + 175 / (x + 6) = 10

175 (x - 6) + 175 (x + 6) = 10 (x - 6) (x + 6)

175x - 175 (6) + 175x + 175 (6) = 10 (x^2 - 36)

350x = 10x^2 - 360

10x^2 - 350x - 360 = 0

x^2 - 35x - 36 = 0 - I saw that 10 will divide out to make my life easier

(x - 36) (x + 1) = 0

x - 36 = 0 x + 1 = 0

x = 36 x = - 1 (Throw this one out)

The canoe travels 36 miles per hour in still water