Question

A car travels $100km$ at a speed of $60km/h$ and returns with a speed of $40km/h$. Calculate the average speed for the whole journey.

Answer 1

In the first case, car travels at a speed of $60km/h$ for a distance of $100km$
In the second case, car travels at a speed of $40km/h$ for a distance of $100km$
Total distance travelled $=200km$
In the first case, car travels at a speed of $60km/h$ for a distance of $100km$
$Speed=\frac{Distance}{Time}$
$Time=\frac{Distance}{Speed}$
$t_1=\frac{100}{60}h$
In the second case, car travels at a speed of $40km/h$ for a distance of $100km$
$t_2=\frac{100}{40}h$
Total distance travelled $=200km$
total time taken $=\frac{100}{60}+\frac{100}{40}$
Average speed $=\frac{\text{Total distance travelled}}{\text{Total time taken}}$
$=\frac{200}{\frac{100}{60}+\frac{100}{40}}=\frac{2}{\frac{1}{60}+\frac{1}{40}}$
$=\frac{4800}{100}=48km/h$