A train travels some distance with a speed of 30 km per hour and returns with a speed of 45 kilometre per hour calculate the average speed of the train
Answers
A train travels some distance with a speed of 30 km per hour and returns with a speed of 45 kilometre per hour calculate the average speed of the train .
We have to find the average speed of the train.
Let us assume that the distance covered by the train is 'x' km.
Average speed is defined as the ratio of total distance covered with respect to total time taken.
Total distance covered by the train = (x + x) km = (2x) km
Also,
Time = Distance/Speed
Case 1:
t1 = x/30 hr
Case 2:
t2 = x/45 hr
Total time = t1 + t2
= x/30 + x/45
= (3x + 2x)/90
= 5x/90
Therefore, Average speed of the train = (Total distance covered)/(Total time taken)
= 2x/(5x/90)
= (2x × 90)/5x
= 2*18 = 36 km/hr
Therefore, 36 km/hr is the average speed of the train.
Shortcut Method:
S1 = 30 km/hr and S2 = 45 km/hr
Average speed = (2 × S1 × S2)/(S1 + S2)
= (2 × 30 × 45)/(30 + 45)
= 2700/75
= 36 km/hr
Therefore, 36 km/hr is the average speed of the train.