A boy travelling at 3 km/h reaches his school 32 minutes late. If he travels at 5 km/h, he reaches his school 28 minutes early. Find the distance he travels every day to reach the school.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7.5 km
The distance is the same both ways, and the two journey times differ by 32 + 28 = 60 minutes: being 32 minutes late at the slow speed and 28 minutes early at the fast speed.
Taking the distance as \(d\) km:
Time at 3 km/h \(\displaystyle =\frac{d}{3}\) h; time at 5 km/h \(\displaystyle =\frac{d}{5}\) h
\(\displaystyle \frac{d}{3}-\frac{d}{5}=1\), so \(\displaystyle \frac{2d}{15}=1\)
\(\displaystyle d=\frac{15}{2}=7.5\) km