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

Step 1: Set up the time equations.
Let the distance to be walked be \(x\) km, and let the scheduled time to reach on time be \(T\) hours.
Walking at 4 km/h makes me 15 minutes (\(\frac{1}{4}\) hour) late, so the time taken is \(T + \frac{1}{4}\) hours:
\[ \frac{x}{4} = T + \frac{1}{4} \]
Walking at 6 km/h makes me 10 minutes (\(\frac{1}{6}\) hour) early, so the time taken is \(T - \frac{1}{6}\) hours:
\[ \frac{x}{6} = T - \frac{1}{6} \]

Step 2: Eliminate \(T\) and solve for \(x\).
Subtracting the second equation from the first:
\[ \frac{x}{4} - \frac{x}{6} = \frac{1}{4} + \frac{1}{6} \]
\[ \frac{3x - 2x}{12} = \frac{3+2}{12} \]
\[ \frac{x}{12} = \frac{5}{12} \]
\[ x = 5 \]

Final Answer:
The distance to be walked is 5 km. Checking: at 4 km/h, time = 5/4 = 1.25 h; at 6 km/h, time = 5/6 is about 0.833 h; the difference is 1.25 - 0.833 = 0.417 h is about 25 min, which matches the total gap of 15 + 10 = 25 minutes between the two scenarios. \[ \boxed{x = 5 \text{ km}} \]