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

https://shopify.pxf.io/c/4884043/1465639/13624

ALITER:

$${Average \ speed =\frac{2v_1v_2}{v_1+v_2}} $$

$${Average \ speed=\frac{2(40)(60)}{100}}$$

$${Average \ speed=\frac{480}{100}}$$

$${Average \ speed=48 \ \frac{Km}{h}}$$

Links to this post

Average Speed Calculation: Particle’s Journey Explained

Average Speed of a Car Traveling at Varying Speeds | Calculation & Concept