Problema Solution

A kayaker can row 6 miles upstream, against a 2mph current, in one hour more than he can row 7 miles downstream. What is his average speed in still water?

Answer provided by our tutors

let the still water speed be v


Upstream travel - Downstream travel = 1

where upstream travel is 6/(v-2)

and downstream travel is 7/(v+2)


this gives the equation:

6/(v-2) - 7/(v+2) = 1

[6v+12 - 7v + 14]/[v^2 - 4] = 1

-v + 26 = v^2 - 4

giving the quadratic equation:

v^2 + v - 30 = 0


Solving this equation gives a solution set of {5, -6}, so the still water velocity is the positive value, 5mph