A car travels a straight road at 20 km/h for the first quarter of the distance and at 40 km/h for the remaining three quarters. Find its average speed for the whole road.

Step-by-step solution

1. 1

   Introduce the unknown total distance. Let the road be $s$ kilometres long. Because only fractions of the distance are given, $s$ will cancel at the end, so any symbol works.

2. 2

   Time the first quarter. $t_1=\frac{s/4}{20}=\frac{s}{80}$

3. 3

   Time the remaining three quarters. $t_2=\frac{3s/4}{40}=\frac{3s}{160}$

4. 4

   Add the times over a common denominator. $t=\frac{s}{80}+\frac{3s}{160}=\frac{2s+3s}{160}=\frac{5s}{160}=\frac{s}{32}$

5. 5

   Divide total distance by total time. $v_{tb}=\frac{s}{s/32}=32\text{ km/h}$ The $s$ cancels, so the answer is B. The distance-weighted mean $\tfrac14(20)+\tfrac34(40)=35\text{ km/h}$ is not valid here, because slow kilometres eat more time than fast ones.