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: Compare the two speeds as a ratio.
The speeds are 48 kmph and 36 kmph. Dividing both by 12, the ratio of speeds is $48:36 = 4:3$.

Step 2: Convert the speed ratio into a time ratio.
For a fixed distance, time taken is inversely proportional to speed, so a speed ratio of $4:3$ corresponds to a time ratio of $3:4$ (the faster speed takes the smaller share of time).
Let the time at 48 kmph be $3k$ hours and the time at 36 kmph be $4k$ hours, for some constant $k$.

Step 3: Use the 15 minute delay to find k.
The difference between the two times is 15 minutes, which is $\frac{1}{4}$ hour.
\[ 4k - 3k = \frac{1}{4} \]
\[ k = \frac{1}{4} \]

Step 4: Find the actual time and then the distance.
Time at 48 kmph is $3k = 3 \times \frac{1}{4} = \frac{3}{4}$ hour, which is 45 minutes.
Distance $= \text{speed} \times \text{time} = 48 \times \frac{3}{4} = 36$ km.

Final Answer:
Using the speed-to-time ratio method also gives a journey distance of 36 km. \[ \boxed{36 \text{ km}} \]