Question

What speed would the motorist have to average on the return trip from B to A to yield an overall speed of 30km per hour ( assume the motorist has average 20km per hour from A to B)

Answer 1

We denote by $l$ the distance between A and B. Then for the trip from A to B he spent $\frac{l}{20}$ hours. We denote by $v$ his average speed on the return trip. The time he used on the return trip is $\frac{l}{v}$ hours. Since the overall speed of the motorist is 30 km per hour, we get the equation for $v$:

$30=\frac{2l}{\frac{l}{20}+\frac{l}{v}}\,\,\Longrightarrow\,\,30=\frac{40v}{20+v}\,\,\Longrightarrow 600=10\,v\,\,\Longrightarrow v=60 \,\,\textrm{km\,\, per\,\, hour}$

Answer: 60 km per hour