Question

I have to reach a certain place at a certain time and I find that I shall be 15 min too late, if I walk at 4 km an hour, and 10 min too soon, if I walk at 6 km an hour. How far have I to walk?

• A. 25 km
• B. 5 km
• C. 10 km
• D. none of these

Hint:

The gap between being 15 minutes late and 10 minutes early is 25 minutes, use this directly as the difference between the two travel times.

Answer 1

The Correct Option is B

A slightly faster way avoids introducing the scheduled time T explicitly by working directly with the total time gap between the two walking speeds.

1. Find the total time gap: walking at 4 km/h makes me 15 minutes late, and walking at 6 km/h makes me 10 minutes early. The difference between these two travel times is therefore 15 + 10 = 25 minutes = \( \dfrac{5}{12}\) hour, since the gap spans both the late amount and the early amount relative to the correct on-time arrival.
2. Express this gap using the distance: if \(x\) is the distance, the time taken at 4 km/h minus the time taken at 6 km/h equals this same gap:
   \[ \frac{x}{4} - \frac{x}{6} = \frac{5}{12} \]
3. Solve for x: \( \dfrac{3x-2x}{12} = \dfrac{5}{12}\), so \( \dfrac{x}{12} = \dfrac{5}{12}\), giving \(x = 5\).

This confirms the distance is 5 km, matching option B, without needing to solve for the scheduled time T separately.