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

Answer 1

The Correct Option is B

To solve this problem, we need to determine the distance using the information provided about the speeds and time differences. Let's denote the distance to walk as \( d \) kilometers. First, convert the time differences into hours since speed is given in kilometers per hour.

The given conditions are:

• Walking at 4 km/h results in being 15 minutes late.
• Walking at 6 km/h results in being 10 minutes early.

Convert minutes to hours:

• 15 minutes = \( \frac{15}{60} = \frac{1}{4} \) hour
• 10 minutes = \( \frac{10}{60} = \frac{1}{6} \) hour

Let t be the time (in hours) it should take to reach the destination on time. The equations from the problem statement are:

• If walking at 4 km/h: \( \frac{d}{4} = t + \frac{1}{4} \)
• If walking at 6 km/h: \( \frac{d}{6} = t - \frac{1}{6} \)

From the two equations:

1. \( \frac{d}{4} - \frac{d}{6} = \frac{1}{4} + \frac{1}{6} \)
2. Find a common denominator for the fractions:

(The common denominator of 4 and 6 is 12.)

• \( \frac{3d}{12} - \frac{2d}{12} = \frac{3}{12} + \frac{2}{12} \)
• \( \frac{1d}{12} = \frac{5}{12} \)

Solving for d:

• Multiply both sides by 12: \( d = 5 \)

Thus, the distance \( d \) you have to walk is 5 kilometers.