Three-eighth of a journey is covered at a speed of 60 km/hr, and the remaining distance is covered at the rate of 40 km/hr. The average speed for the whole journey (in km/hr, rounded off to the nearest integer) is:

Correct option is B

Given:

3/8 of the journey is covered at 60 km/h.

The remaining 5/8 of the journey is covered at 40 km/h.

Formula Used:

Average speed = Total distance / Total time

Solution:

Let the total distance be d km

​$$\text{Time}_1 = \frac{3d}{8} \div 60 = \frac{d}{160}$$​​

​$$\text{Time}_2 = \frac{5d}{8} \div 40 = \frac{5d}{320} = \frac{d}{64}$$​​

Total time = $$\frac{d}{160} + \frac{d}{64}$$​​

​$$= \left( \frac{1}{160} + \frac{2.5}{160} \right)$$​​

​$$= \left( \frac{3.5}{160} \right)$$​​

​$$= \frac{7d}{320}$$​​

Average speed = $$\frac{d}{\frac{7d}{320}}$$​​

​$$= \frac{320}{7}$$​​

= $$45.714 \approx 46\ \text{km/h}$$​​