Answer
The average speed is $~~25.45~km/h$
Work Step by Step
Let $d$ be the distance up the hill.
We can find the time for the cart to travel up the hill:
$t = \frac{d}{v} = \frac{d}{20}$
We can find the time for the cart to travel down the hill:
$t = \frac{d}{v} = \frac{d}{35}$
We can find the total time of the return trip:
$t = \frac{d}{20}+\frac{d}{35}$
$t = \frac{7d}{140}+\frac{4d}{140}$
$t = \frac{11d}{140}$
We can find the average speed of the return trip:
$v_{ave} = \frac{2d}{t}$
$v_{ave} = \frac{2d}{\frac{11d}{140}}$
$v_{ave} = \frac{(2d)(140)}{11d}$
$v_{ave} = \frac{280}{11}$
$v_{ave} = 25.45~km/h$
The average speed is $~~25.45~km/h$
