Question:
A car covers the first half of the distance between two places at a speed 40 Kmh-1 and the second half 60 Kmh-1.What is the average speed of the car?
Solution:
$${Average \ speed = \frac{Total \ distance} {Total \ time \ taken}}$$
Let the distance between the two places be ‘2d’ Km
Time taken by the car to cover the first half of the journey
$${time =\frac{distance}{speed}=\frac {d}{40} \ hr}$$
And, time taken by the carto cover the remaining second half of the jorney
$${time =\frac{distance}{speed}=\frac {d}{60} \ hr}$$
The total time of the journey
$${=\frac{d}{40}+\frac{d}{60}=\frac{3d+2d}{120}}$$
$${Total \ time =\frac{5d}{120} \ hr} $$
$${Average \ speed =\frac{Total \ distance}{Total \ time}} $$
$${Average \ speed=\frac{2d}{\frac{5d}{120}}}$$
$${Average \ speed =\frac{240}{5}}$$
$${Average speed=48 \ \frac{Km}{h}}$$
The average speed of the car is 48 Kmh-1
ALITER:
$${Average \ speed =\frac{2v_1v_2}{v_1+v_2}} $$
$${Average \ speed=\frac{2(40)(60)}{100}}$$
$${Average \ speed=\frac{480}{100}}$$
$${Average \ speed=48 \ \frac{Km}{h}}$$