Question

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

Answer 1

Time taken by the car to cover the first 100 km of the journey = $\frac{\mathrm{Distance}\mathrm{travelled}}{\mathrm{Speed}}=\frac{100\mathrm{km}}{60\mathrm{km}/\mathrm{h}}=\frac{5}{3}\mathrm{h}$


Time taken by the car to return the same distance = $\frac{\mathrm{Distance}\mathrm{travelled}}{\mathrm{Speed}}=\frac{100\mathrm{km}}{40\mathrm{km}/\mathrm{h}}=\frac{5}{2}\mathrm{h}$

Total distance travelled by car in the whole journey = 200 km


Total time taken by the car to complete the whole journey = $\frac{5}{3}\mathrm{h}+\frac{5}{2}\mathrm{h}=\frac{125}{6}\mathrm{h}$

The average speed of the whole journey = $\frac{\mathrm{Total}\mathrm{distance}\mathrm{travelled}}{\mathrm{Total}\hspace{0.17em}\mathrm{time}\mathrm{taken}}=\frac{200\mathrm{km}}{{\displaystyle \frac{125}{6}\mathrm{h}}}=\frac{200\times 6}{125}\mathrm{km}/\mathrm{h}=9.6\mathrm{km}/\mathrm{h}$

Hence, the car covers the whole journey at an average speed of 9.6 km/h.