A man travelled from the village to the post-office at the rate of 25 km/hr and walked back at the rate of 4 km/hr. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 20 km
Step 1: Let the distance of the post office = x km
- Speed going = 25 km/h → time = x/25 hours
- Speed returning = 4 km/h → time = x/4 hours
Total time = 5 hours 48 minutes = 5 + 48/60 = 5.8 hours
$\frac{x}{25} + \frac{x}{4} = 5.8$
Step 2: Find a common denominator
$\frac{x}{25} + \frac{x}{4} = \frac{4x + 25x}{100} = \frac{29x}{100} = 5.8$
$29x=5.8 29x=5.8×100=580$
$29x=5.8×100=580$
$x = \frac{580}{29} = 20 \ \text{km}$