Question

A car covers the first half of the distance between two places at 40 km/h and another half at 60 km/h. The average speed of the car is

• A. 40 km/h
• B. 48 km/h
• C. 50 km/h
• D. 60 km/h

Answer 1

The Correct Option is B

To find the average speed of the car over the entire journey, we need to consider both halves of the journey it makes. Let's break down the problem step by step.

1. Assume the total distance between the two places is D. Therefore, each half of the distance is \frac{D}{2}.
2. The car covers the first half of the distance, \frac{D}{2}, at a speed of 40 km/h. The time taken to cover this part is given by:

T_1 = \frac{\frac{D}{2}}{40} = \frac{D}{80}

3. The car covers the second half of the distance, \frac{D}{2}, at a speed of 60 km/h. The time taken to cover this part is given by:

T_2 = \frac{\frac{D}{2}}{60} = \frac{D}{120}

4. Total time for the journey is the sum of T_1 and T_2:

T_{\text{total}} = T_1 + T_2 = \frac{D}{80} + \frac{D}{120}

To add these fractions, find a common denominator, which is 240:

T_{\text{total}} = \frac{3D}{240} + \frac{2D}{240} = \frac{5D}{240}

5. The average speed is the total distance divided by the total time:

\text{Average Speed} = \frac{D}{T_{\text{total}}} = \frac{D}{\frac{5D}{240}} = \frac{240}{5} = 48 \text{ km/h}

Therefore, the average speed of the car over the entire journey is 48 km/h, which matches the correct option.