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