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. \( 10 \, \text{km} \)
• B. \( 12 \, \text{km} \)
• C. \( 15 \, \text{km} \)
• D. \( 20 \, \text{km} \)

Hint:

When dealing with time, speed, and distance problems, use the formula \( \text{time} = \frac{\text{distance}}{\text{speed}} \) to create equations. If you know the time difference, subtract the two equations to solve for the unknown distance.

Answer 1

The Correct Option is A

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: \[ \frac{5d - 4d}{20} = \frac{1}{2} \] \[ \frac{d}{20} = \frac{1}{2} \] \[ d = 10 \, \text{km} \] Final Answer: The correct answer is (a) \( 10 \, \text{km} \).