Sourav completes a journey in \(5\frac{1}{2}\) hours. If he covers half of the distance at 5 km/h and the remaining distance at 6 km/h, then find the total distance covered by him.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 30 km
For each half of the journey, time = distance ÷ speed; the two times add up to the whole journey time of \(5\frac{1}{2}\) hours.
Assuming the total distance to be \(d\) km:
Time for the first half at 5 km/h: \(\displaystyle\frac{d/2}{5}=\frac{d}{10}\) hours
Time for the second half at 6 km/h: \(\displaystyle\frac{d/2}{6}=\frac{d}{12}\) hours
Total time: \(\displaystyle\frac{d}{10}+\frac{d}{12}=\frac{11}{2}\)
\(\displaystyle\frac{11d}{60}=\frac{11}{2}\), so \(d=30\) km
Shortcut:
For two equal distances, the average speed is \(\displaystyle\frac{2\times5\times6}{5+6}=\frac{60}{11}\) km/h
Distance \(=\displaystyle\frac{60}{11}\times\frac{11}{2}=30\) km