Question

A man can cover a distance in 1 hour 24 minutes by covering 2/3 of the distance at 4 km/h and the rest at 5 km/h. The total distance is

• A. 2 km
• B. 5 km
• C. 6 km
• D. 10 km
• E. None of these

Hint:

For mixed-speed problems, break down the time for each part of the journey and then solve for the total distance using the total time.

Answer 1

The Correct Option is C

Let the total distance be \( d \). The man covers \( \frac{2}{3} \) of the distance at 4 km/h and \( \frac{1}{3} \) at 5 km/h. Time taken for first part: \[ \text{Time} = \frac{\frac{2}{3}d}{4} = \frac{d}{6} \] Time taken for second part: \[ \text{Time} = \frac{\frac{1}{3}d}{5} = \frac{d}{15} \] Total time: \[ \frac{d}{6} + \frac{d}{15} = \frac{1}{6}d + \frac{1}{15}d = \frac{5d + 2d}{30} = \frac{7d}{30} \] We are told the total time is 1 hour 24 minutes, which is \( \frac{7}{5} \) hours. Thus: \[ \frac{7d}{30} = \frac{7}{5} \] Solving for \( d \): \[ d = \frac{30}{5} = 6 \, \text{km} \]