question_answer

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

A) 32.7 km/h

B)                        35 km/h              

C)        40 km/h              

D)        45 km/h

Correct Answer: A

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 \[=\frac{S}{\frac{S/3}{20}+\frac{S/3}{40}+\frac{S/3}{60}}\]                                 \[=\frac{3}{\frac{1}{20}+\frac{1}{40}+\frac{1}{60}}\]                                 \[=\frac{3}{\left( \frac{6+3+2}{120} \right)}\] \[=\frac{3\times 120}{11}=32.7\,\text{km/h}\]