Question

A train travels from one station to another at a speed of 40 km/hour and returns to the first station at a speed of 60 km/hr.What is the average speed of the train?

Answer 1

☯ AnSwEr :

As, the coming distance and returning distance is same. But, speed is different & we have to find the average speed of the train.

So,

Let the distance between both the stations be x.

$\therefore$ Total distance taken = 2d ....(1)

$\rule{150}{2}$

Now,

Initial velocity(u) = 40 km/h

Time taken for initial velocity $\sf{{t_1} = \frac{x}{40}}$

Final velocity(v) = 60 km/h

Time taken for final velocity $\sf{{t_2} = \frac{x}{60}}$

$\sf{\dashrightarrow Total \: time \: taken = \frac{x}{60} + \frac{x}{40}} \\ \\ \sf{\dashrightarrow Total \: time \: taken = \frac{2x + 3x}{120}} \\ \\ \sf{\dashrightarrow Total \: time \: taken =\frac{5x}{120}} \\ \\ \sf{\dashrightarrow Total \: time \: taken = \frac{x}{24}.....(2)}$

$\rule{200}{2}$

We know that,

$\large{\implies{\boxed{\boxed{\sf{Average \: speed = \frac{Total \: Distance \: travelled}{Total \: time \: taken}}}}}}$

★ Putting Values ★

$\sf{\dashrightarrow Average \: speed = \dfrac{\dfrac{2x}{x}}{24}}\\ \\ \sf{\dashrightarrow Average \: speed = 2 \times 24} \\ \\ \sf{\dashrightarrow Average \: speed = 48 \: kmh^{-1}} \\ \\ \Large{\implies{\boxed{\boxed{\sf{Average \: speed = 48 \: Kmh^{-1}}}}}}$