A cyclist travels from point A to B and back from B to A along the same route. On the onward journey, he covers one-third of the distance at 12 km/hr and the remaining distance at 18 km/hr. On the return journey, he covers half of the distance at 9 km/hr and the remaining distance at 18 km/hr. Find the average speed (in km/hr) for the entire round trip.
13.5 km/hr
Let the one-way distance be D. Onward: \(\tfrac{D}{3}\) at 12 km/hr takes \(\tfrac{D}{36}\) hr, and \(\tfrac{2D}{3}\) at 18 km/hr takes \(\tfrac{D}{27}\) hr.
Return: \(\tfrac{D}{2}\) at 9 km/hr takes \(\tfrac{D}{18}\) hr, and \(\tfrac{D}{2}\) at 18 km/hr takes \(\tfrac{D}{36}\) hr.
Taking D=18 km for ease: onward time \(=0.5+0.667=1.167\) hr; return time \(=1+0.5=1.5\) hr.
Total distance \(=36\) km; total time \(=2.667\) hr.
Average speed: \(\dfrac{36}{2.667} = 13.5\) km/hr.
Hence, the average speed for the entire round trip is 13.5 km/hr.
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Important Questions from Average Speed
A car runs first 275 km at an average speed of 50 km/h and the next 315 km at an average speed of 70 km/h. What is the average speed ( in km/h) for the entire journey?
Akhil rides first 12 km at a speed of 16 km/h and further 6 km at a speed of 20 km/h. Find his average speed (in km/h).
Shyam drives his car 30 km at a speed of 45 km/h and, for the next 1 h 20 m, he drives it at a speed of 51 km/h. Find his average speed (in km/h) for the entire journey.
X and Y travel a distance of 90 km each such that the speed of Y is greater than that of X. The sum of their speeds is 100 km/h and the total time taken by both is 3 hours 45 minutes. The ratio of the speed of X to that of Y is:
If a man travels at \(\frac{1}{x}\) km/h on a journey and returns at \(\rm \frac{1}{x^2}\) km/h, then his average speed for the journey is:
