A and B started together to cover a certain distance, at a speed of 8 km/h and 10 km/h, respectively. If A arrives 15 minutes after B, then find the distance.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10 km
Time taken is distance divided by speed. Both cover the same distance \(d\), and A, the slower one, takes 15 minutes \(=\frac{1}{4}\) hour longer, so A’s time minus B’s time is \(\frac{1}{4}\) h.
Time taken by A \(=\frac{d}{8}\) h; time taken by B \(=\frac{d}{10}\) h
A takes \(\frac{1}{4}\) h more: \(\displaystyle \frac{d}{8}-\frac{d}{10}=\frac{1}{4}\)
\(\displaystyle \frac{5d-4d}{40}=\frac{d}{40}=\frac{1}{4}\), so \(d=\frac{40}{4}=10\) km
Shortcut: For one distance covered at two speeds, distance \(=\) product of the speeds \(\div\) difference of the speeds \(\times\) difference in time.
\(\displaystyle \frac{8\times10}{10-8}\times\frac{1}{4}=40\times\frac{1}{4}=10\) km