Q:Related rates problem Question: A person can swim from A to B (with current) in 40 minutes, and back (against current) in 45 minutes. How long does it take them to kayak from A to B if the return trip (B to A, against current) takes 15 minutes.
Assume the speed of the current, and swim and kayaking speeds relative to current are all constant.
I set up the following equations, and tried to solve:
x = distance (constant), y = swim speed, z = current, a = kayak speed
t = time to get from B to A kayaking

*

*$x = 45(y-z)$

*$x= 15(a-z)$

*$x = 40(y+z)$

*$x = s (a + z)$
I got y = 17z from 1 and 3, and tried to create a proportion from them and use that to get the kayaking time, but it that didn't work.
Any ideas? Any and all help is appreciated.

Let x be 1.
The kayaking rate is unaffected by the swim speed, only the current, so you should solve for the current, z, with Equations 1 and 3.
As a hint, don't do 45(y-z)=40(y+z), as that will give you z in terms of y when you can solve for z itself.
Assuming s is the kayaking time from A to B, notice equations 2 and 4 are two equations with 2 unknowns after you find z, namely a and s.
Can you take it from here?
