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A car travels up a hill at the constant speed of 40 km/h and returns down the hill at the speed of 60 km/h. Calculate the average speed for the round trip.

A car travels up a hill at the constant speed of 40 km/h and returns down the hill at the speed of 60 km/h. Calculate the average speed for the round trip.

Grade:11

2 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
Let us assume that the distance travelled by the car in travelling up or down the hill is s. Let the time taken by the car to travel up the hill with speed v1 is t1 whereas the time taken by the car to travel down the hill with speed v2 is t2.
Given:
Speed with which car travels up the hill, v1 = 40 km/h vl
Speed with which car travels down the hill, v2 = 60 km / h
The average speed of the car for the round trip is given as:

236-2393_average speed.JPG
The total distance travelled by the car in a round trip is twice the distance it travelled up or down the hill that is 2s.

236-1119_average speed 2.JPG….….….….….….….…...(1)
The elapsed time for the round trip is the sum of the time (t1) taken to travel up the hill and time (t2) to travel down the hill. Therefore the average speed is given as:
Also the time t1 is given as:
236-1568_distance.JPG
The time t2 is given as:
236-1437_distance 2.JPG
Substitute the value of t1 and t2 in equation (1) to get:
236-1753_average 3.JPG
Substitute the given values of v1 and v2 to get the average speed of round trip as:
236-355_average4.JPG
Therefore the average speed of the car for the round trip is. 48 km/h.
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the attached solution to your problem.
 
Let the distance between two ends be ‘s’ and the time for the forward and return journey be t1 and t2 respectively.
236-1753_average 3.JPG
Hence, average speed = 2(40)(60) / [40 + 60]
                                 = 48 km/h
 
Hope it helps.
Thanks and regards,
Kushagra

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