Question

A person reaches his office just in time when he travels at a speed of 48 kmph. When he moves at a speed of 36 kmph, he gets late by 15 minutes. Find the distance of the journey.

• A. 48 km
• B. 36 km
• C. 30 km
• D. 44 km

Hint:

Write the travel time at each speed in terms of the unknown distance, and set their difference equal to 15 minutes converted into hours.

Answer 1

The Correct Option is B

Step 1: Set up the times taken at both speeds.
Let the distance of the journey be \(d\) km.
Time taken at 48 kmph is \(\frac{d}{48}\) hours, and since this gets him there exactly on time, this is also the scheduled travel time.
Time taken at 36 kmph is \(\frac{d}{36}\) hours, and this makes him 15 minutes late.

Step 2: Convert the time difference to hours.
15 minutes is \(\frac{15}{60} = \frac{1}{4}\) hour.
So the time at 36 kmph is \(\frac{1}{4}\) hour more than the time at 48 kmph.
\[ \frac{d}{36} - \frac{d}{48} = \frac{1}{4} \]

Step 3: Simplify the left side using a common denominator.
The LCM of 36 and 48 is 144.
\[ \frac{4d}{144} - \frac{3d}{144} = \frac{1}{4} \]
\[ \frac{d}{144} = \frac{1}{4} \]

Step 4: Solve for d.
\[ d = \frac{144}{4} = 36 \]

Final Answer:
The distance of the journey is 36 km. \[ \boxed{d = 36 \text{ km}} \]