A student goes to school from his residence at a speed of \(2\displaystyle\frac{1}{2}\) km/h and reaches school 6 minutes late. If he travels at a speed of 3 km/h, he reaches 10 minutes before time. What is the distance of his school from his residence?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4 km
The distance is the same on both days, so the difference in the two journey times comes from the two speeds alone. Being 6 minutes late on one day and 10 minutes early on the other means the slower journey takes \(6+10=16\) minutes more.
Assuming the distance to be \(d\) km:
Difference in time: 16 min \(\displaystyle=\frac{16}{60}=\frac{4}{15}\) h
Time at 2.5 km/h minus time at 3 km/h is this difference: \(\displaystyle\frac{d}{2.5}-\frac{d}{3}=\frac{4}{15}\)
\(\displaystyle\frac{2d}{5}-\frac{d}{3}=\frac{d}{15}=\frac{4}{15}\), so the school is 4 km away