Question

A man goes uphill with an average speed of 24 km/h and comes down with an average speed of 36 km/h. The distance travelled in both cases being the same. The average speed for the entire journey is:

• A. 30 km/h
• B. 28.8 km/h
• C. 32 km/h
• D. 45 km/h

Answer 1

The Correct Option is B

To determine the average speed for the entire journey, we need to consider the formula for average speed when the total distance is traveled with different speeds. The average speed \( V_{\text{avg}} \) is given by:

\(V_{\text{avg}} = \frac{2 \cdot S}{\frac{S}{V_1} + \frac{S}{V_2}}\)

where \(S\) is the distance of each segment, \(V_1\) is the uphill speed, and \(V_2\) is the downhill speed.

Given \(V_1 = 24\) km/h and \(V_2 = 36\) km/h, the average speed can be calculated as follows:

\(V_{\text{avg}} = \frac{2 \cdot S}{\frac{S}{24} + \frac{S}{36}} = \frac{2}{\frac{1}{24} + \frac{1}{36}}\)

First, find the sum of the reciprocals:

\(\frac{1}{24} + \frac{1}{36} = \frac{3}{72} + \frac{2}{72} = \frac{5}{72}\)

Now calculate the average speed:

\(V_{\text{avg}} = \frac{2}{\frac{5}{72}} = 2 \cdot \frac{72}{5} = \frac{144}{5} = 28.8\) km/h

Thus, the average speed for the entire journey is 28.8 km/h.