Question

If a man covers 1/3rd of the distances at speeds of 10, 20, and 60 km/hr each. Find his average speed.

• A. 15 km/hr
• B. 20 km/hr
• C. 25 km/hr
• D. 30 km/hr

Hint:

To find average speed for multiple distances, use the formula: \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \]

Answer 1

The Correct Option is B

Let the total distance be \( D \). The man covers 1/3 of the total distance at each of the speeds. So, the time taken for each part of the journey is: \[ t_1 = \frac{D/3}{10}, \quad t_2 = \frac{D/3}{20}, \quad t_3 = \frac{D/3}{60} \] The total time taken is: \[ T = \frac{D}{3} \left( \frac{1}{10} + \frac{1}{20} + \frac{1}{60} \right) = \frac{D}{3} \times \frac{1}{5} = \frac{D}{15} \] The average speed is given by: \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{D}{D/15} = 15 \text{ km/hr} \]