Question

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

Answer 1

Answer: (A)

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