Question

A non-stop bus goes from one station to another station with a speed of 54km hr-1(minus 1).
The same bus returns from the second station to the first station  with a speed of 36km hr-1. find the average speed of the bus for the entire journey.

Answer 1

avg. speed = 2d/(d/36 + d/54) = 2*54*36/(36 + 54) = 2*3*36/5 = 43.2 kmph.

Answer 2

The average speed of the bus average speed is 43.2 km/hr

Given data:

The speed of the non-stop bus from one station = 54 km/h

The bus returns with a speed = 36 km/hr

To find:

Average speed = ?

Solution:

Let us assume that the distance between both the station be x.

In first travel, time taken is given below:

$t_{1}=\frac{x}{54}$

In second travel, time taken is given below:

$t_{2}=\frac{x}{36}$

Therefore, the total time taken is,

$t=t_{1}+t_{2}=\frac{x}{54}+\frac{x}{36}$

Total distance travelled be,

$x + x = 2x$  

Thereby,

$\text {Average speed} = \frac {\text{Total distance}}{\text{Total time}}$

$=\frac{2 x}{\frac{x}{54}+\frac{x}{36}}$

$=\frac{2 x}{\frac{90 x}{54 \times 36}}$

$=2 x \times \frac{1944}{90 x}$

$\Rightarrow \text {Average speed}=43.2 \ \mathrm{km} / \mathrm{hr}$