Lewis drives from London to Brighton at an average speed of $$60\text{mph}$$. On the way back, he gets stuck in traffic and his average speed is only $$40\text{mph}$$. What is his average speed for the whole journey? 
Overseas Competition->Knowledge Point->Distance Word Problems->Bus Departure Time Word Problems
Let the distance from London to Brighton be $$d$$ miles. Since time $$=$$ distance $$\div$$ speed, the times Lewis spent on the two parts of his journey are $$\frac{d}{60}$$ hours and $$\frac{d}{40}$$ hours. Hence the total time in hours that he travelled is$$\frac{d}{60}+ \frac{d}{40}= \frac{2d+3d}{120}= \frac{5d}{120}= \frac{d}{24}$$.  Therefore his average speed for the whole journey is $$2d \div \left( \frac{d}{24}\right)\text{mph}=48 \text{mph}$$. 