Question

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?

Answer 1

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