A motorist travels a certain journey in two stages. In the first stage, he travels for one-third of the total time at 30 km/hr. In the second stage, he travels for the rest of the time at 60 km/hr. He returns to the start at a uniform speed of 75 km/hr. What is the average speed for the entire round trip?
60 km/hr
Let the total time of the onward journey be \(3t\). First stage: time \(t\) at 30 km/hr covers \(30t\) km.
Second stage: time \(2t\) at 60 km/hr covers \(120t\) km. Onward distance = \(30t + 120t = 150t\) km.
Onward average speed = \(\frac{150t}{3t} = 50\) km/hr; the return covers the same \(150t\) km at 75 km/hr taking \(\frac{150t}{75} = 2t\).
Total distance = \(2 \times 150t = 300t\); total time = \(3t + 2t = 5t\).
Average speed of round trip = \(\frac{300t}{5t} = 60\) km/hr.
Hence, the average speed for the entire round trip is 60 km/hr.
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Important Questions from Average Speed
A person covers a certain distance at the speed of 60 kmph and returns to the starting point at a speed of 40 kmph . Find the average speed (in km/hour) of the person for the whole journey.
A train runs at a speed of 28 kmph for 4 hours and 30 kmph for 5 hours and the remaining 40 kms in one hour. What is the average speed per hour?
Kapil travels for 4.5 hours at a speed of 50 km / h and 7.5 hours at a speed of 70 km / h. At the end of it, he finds that he covered only 6/7 of the total distance. At what average speed should he travel so that the remaining distance traveled in 5 hours?
A car has to cover 125 kms in 5 hours. What will be the average speed of the car if it has covered 90 kms in the first 3 hours?
A scooter from P to Q travels at 40 km/h and from Q to P at 30 km/h. What is the average speed of the scooter?
