Q. If the first one-third of a journey is travelled at20 km/h, next one-third at 40 km/h and the last one-third at 60 km/h. The average speed of whole journey will be
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Solution:
Key Idea: Average speed is defined as the ratio of total distance travelled by total time taken. Let $ {{t}_{1}},{{t}_{2}},{{t}_{3}} $ be the time taken in travelling distances $ \frac{S}{3},\frac{S}{3},\frac{S}{3}. $ Then
$ {{t}_{1}}=\frac{S/3}{{{v}_{1}}}=\frac{S/3}{20},{{t}_{2}}=\frac{S/3}{{{v}_{2}}}=\frac{S/3}{40}, $ $ {{t}_{3}}=\frac{S/3}{{{v}_{3}}}=\frac{S/3}{60} $ $ \therefore $ Average speed $ =\frac{S}{\frac{S/3}{20}+\frac{S/3}{40}+\frac{S/3}{60}} $ $ =\frac{3}{\frac{1}{20}+\frac{1}{40}+\frac{1}{60}} $ $ =\frac{3}{\left( \frac{6+3+2}{120} \right)} $ $ =\frac{3\times 120}{11}=32.7\,\text{km/h} $
