A man goes up a hill at 18 kmph and comes down at 24 kmph along the same path. What is his average speed?A)20.57km/hrB)26km/hrC)15km/hrD)None of these.

1. Break Down the Problem

To determine the average speed of the man going up and down the hill, we need to use the formula for average speed when traveling the same distance at different speeds.

2. Relevant Concepts

The average speed $V_{avg}$ when the distance is the same but the speeds are different can be calculated using the harmonic mean:

$V_{avg} = \frac{2ab}{a + b}$

where:

• $a$ is the speed going up the hill (18 km/h).
• $b$ is the speed coming down the hill (24 km/h).

3. Analysis and Detail

Let's calculate the average speed using the formula:

$V_{avg} = \frac{2 \cdot 18 \cdot 24}{18 + 24}$

Calculating the denominator:

$18 + 24 = 42$

Calculating the numerator:

$2 \cdot 18 \cdot 24 = 864$

Now, substituting these values into the average speed formula:

$V_{avg} = \frac{864}{42} \approx 20.57$

4. Verify and Summarize

The calculated average speed is approximately 20.57 km/h, which matches one of the given options.

Final Answer

The average speed is approximately 20.57 km/hr (Option A).