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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.

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Solution

## (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: $\mathrm{Time}=\frac{\mathrm{Distance}\mathrm{travelled}}{\mathrm{Speed}}\phantom{\rule{0ex}{0ex}}\mathrm{So},\phantom{\rule{0ex}{0ex}}{t}_{1}=\frac{15}{30}\mathrm{hr}\phantom{\rule{0ex}{0ex}}=\overline{)0.5\mathrm{hr}}$ (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: $\mathrm{Time}=\frac{\mathrm{Distance}\mathrm{travelled}}{\mathrm{Speed}}\phantom{\rule{0ex}{0ex}}\mathrm{So},\phantom{\rule{0ex}{0ex}}{t}_{2}=\frac{75}{50}\mathrm{hr}\phantom{\rule{0ex}{0ex}}=\overline{)1.5\mathrm{hr}}$ (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: $\mathrm{Time}=\frac{\mathrm{Distance}\mathrm{travelled}}{\mathrm{Speed}}\phantom{\rule{0ex}{0ex}}\mathrm{So},\phantom{\rule{0ex}{0ex}}t3=\frac{10}{20}\mathrm{hr}\phantom{\rule{0ex}{0ex}}=\overline{)0.5\mathrm{hr}}$ 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. $=\frac{100}{2.5}\phantom{\rule{0ex}{0ex}}=\overline{)40\mathrm{km}/\mathrm{hr}}$

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