Question

A train travels the first 15 km at a uniform speed of 30 km/h; the next 75 km at a uniform speed of 50 km/h; and the last 10 km at a uniform speed of 20 km/h. Calculate the average speed for the entire train journey.

Answer 1

(i) In the first case, the train travels at a speed of 30 km/h for a distance of 15 km.
We can find the time as:
$$\begin{gathered} \mathrm{Time}=\frac{\mathrm{Distance}\mathrm{travelled}}{\mathrm{Speed}} \\ \mathrm{So}, \\ {t}_1=\frac{15}{30}\mathrm{hr} \\ =\boxed{0.5\mathrm{hr}} \end{gathered}$$

(ii) In the second case, the train travels at a speed of 50 km/h for a distance of 75 km.
We can find the time as:
$$\begin{gathered} \mathrm{Time}=\frac{\mathrm{Distance}\mathrm{travelled}}{\mathrm{Speed}} \\ \mathrm{So}, \\ {t}_2=\frac{75}{50}\mathrm{hr} \\ =\boxed{1.5\mathrm{hr}} \end{gathered}$$

(iii) In the third case, the train travels at a speed of 20 km/h for a distance of 10 km.
We can find the time as:
$$\begin{gathered} \mathrm{Time}=\frac{\mathrm{Distance}\mathrm{travelled}}{\mathrm{Speed}} \\ \mathrm{So}, \\ t3=\frac{10}{20}\mathrm{hr} \\ =\boxed{0.5\mathrm{hr}} \end{gathered}$$

Total distance covered:
= (15 + 75 + 10) km
= 100 km
Total time taken = (0.5 + 1.5 + 0.5) km
= 2.5
Therefore, $\mathrm{Average}\mathrm{speed}=\frac{\mathrm{Total}\mathrm{distance}\mathrm{travelled}}{\mathrm{Time}}$
Now, put the values to get the average speed.
$$\begin{gathered} =\frac{100}{2.5} \\ =\boxed{40\mathrm{km}/\mathrm{hr}} \end{gathered}$$