A motor car covered a certain distance in 9 hours, the first half distance at 12 km/h and the second half distance at 15 km/h. Find the total distance covered.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 120 km
The total time is the sum of the times for the two halves, and each time is distance divided by speed. Let the total distance be \(d\) km, so each half is \(\frac{d}{2}\) km.
Time for the first half at 12 km/h: \(\displaystyle \frac{d}{24}\) h
Time for the second half at 15 km/h: \(\displaystyle \frac{d}{30}\) h
\(\displaystyle \frac{d}{24}+\frac{d}{30}=9\)
\(\displaystyle \frac{5d+4d}{120}=9\), so \(9d=1080\) and \(d=120\) km
Shortcut: For two equal distances, the average speed is \(\frac{2ab}{a+b}\).
Average speed \(\displaystyle =\frac{2\times12\times15}{12+15}=\frac{360}{27}=\frac{40}{3}\) km/h
Distance \(\displaystyle =\frac{40}{3}\times9=120\) km