A man travelled a certain distance by bus at the rate of 40 km/h and returned walking at the rate of 5 km/h via the same route. If the two-way journey took him a total of 4 hours 30 minutes, the total distance covered by him in this 4.5 hours was

Correct option is D

Given:

The man traveled a certain distance by bus at a speed of 40 km/h and returned by walking at a speed of 5 km/h

The total time for the two-way journey is 4 hours 30 minutes (4.5 hours)

Formula Used:

Time = $$\frac{\text{Distance}}{\text{Speed}}$$​

Solution:

Let bus speed, b = 40 km/h and the walking speed be w = 5 km/h

Time taken for the journey by bus = $$\frac{d}{40}$$​​

Time taken for the return journey by walking = $$\frac{d}{5}$$​​

​$$\frac{d}{40} + \frac{d}{5} = 4.5$$​

​$$\frac{d}{40} + \frac{d}{5} = 4.5$$​

​$$\frac{d}{40} + \frac{8d}{40} = 4.5$$​

​$$\frac{9d}{40} = 4.5$$​

9d = 4.5 × 40

9d = 180

d = 20

Thus, the one-way distance is 20 km. Therefore, the total distance covered in the two-way journey is 2d = 2 × 20 = 40