A person covers 1/4 of his journey at the speed of 25 km/h, 1/2 of the journey at 40km/h and the remaining at the speed of 50 km/h. Find his average speed per hour for the whole journey (in km/h).
Given:
A person covers 1 / 4 of the journey at a speed of 25 km/hour, 1 / 2 of the journey at a speed of 40 km/hour, and the remaining part at a speed of 50 km/hour.
Used Formula:
Average speed = Total distance / Total time
Calculation:
Let the total distance be D km.
Distance covered at 25 km/hour = D/4 km
Distance covered at 40 km/hour = D/2 km
Distance covered at 50 km/hour = D - (D/4 + D/2) km = D/4 km
Time taken to cover D/4 km at 25 km/hour = (D/4) / 25 = D/100 hours
Time taken to cover D/2 km at 40 km/hour = (D/2) / 40 = D/80 hours
Time taken to cover D/4 km at 50 km/hour = (D/4) / 50 = D/200 hours
Total time = D/100 + D/80 + D/200
⇒ Total time = D (1/100 + 1/80 + 1/200)
⇒ Total time = D (0.01 + 0.0125 + 0.005)
⇒ Total time = D × 0.0275
Average speed = Total distance / Total time
⇒ Average speed = D / (D × 0.0275)
⇒ Average speed = 1 / 0.0275
⇒ Average speed = \(36\frac{4}{11}\) km/hour
∴ The correct answer is option (1).
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?
