Question

Two cyclists start together to travel to a certain destination, one at the rate of 4 kmph and the other at the rate of 5 kmph. Find the distance if the former arrives half an hour after the latter.

• A. 2 km
• B. 10 m
• C. 10000 m
• D. 1 km

Hint:

When solving for time, speed, and distance problems, remember to use the time formula: \( \text{time} = \frac{\text{distance}}{\text{speed}} \). Set up the equations based on the time difference to find the unknown distance.

Answer 1

The Correct Option is C

Let the distance be \( d \) km. We know the time difference is \( \frac{1}{2} \) hour. Setting up the equation using the time formula for both cyclists, we solve for \( d \), which gives \( d = 10 \, \text{km} \). Let the distance be \( d \) km. % Time for the second cyclist The time taken by the second cyclist is \( \frac{d}{5} \) hours. % Time for the first cyclist The time taken by the first cyclist is \( \frac{d}{4} \) hours. We are told that the first cyclist arrives 30 minutes (or \( \frac{1}{2} \) hour) later than the second cyclist. So: \[ \frac{d}{4} - \frac{d}{5} = \frac{1}{2} \] To solve for \( d \), first find a common denominator: \[ \frac{5d - 4d}{20} = \frac{1}{2} \] \[ \frac{d}{20} = \frac{1}{2} \] \[ d = 10 \, \text{km} = 10000 \, \text{m} \] Final Answer: The correct answer is (c) 10000 m.