A train travel some distance with a speed of 30km/hr and return with a speed of 45km/hr. Calculate average speed.
Vavg. = (30+45)/2 = 37.5 km/h.
To calculate the average speed, we need to find the total distance traveled and the total time taken.
Let's assume the distance traveled in one direction is D kilometers. Since the train travels the same distance in the return journey, the total distance traveled is 2D kilometers.
Let's find the time taken for each leg of the trip. The time taken to travel the distance D at a speed of 30 km/hr is given by:
Time taken = Distance / Speed = D / 30
Similarly, the time taken to travel the same distance D at a speed of 45 km/hr is:
Time taken = Distance / Speed = D / 45
The total time taken for both legs of the trip is the sum of the times taken for each leg:
Total time taken = D / 30 + D / 45
To find the average speed, we divide the total distance by the total time taken:
Average speed = Total distance / Total time taken = 2D / (D / 30 + D / 45)
Simplifying the expression, we can write:
Average speed = 2 / (1/30 + 1/45)
To find the average speed, we can calculate the value of the expression 2 / (1/30 + 1/45):
Average speed = 2 / (1/30 + 1/45)
= 2 / (3/90 + 2/90)
= 2 / (5/90)
= 2 * 90 / 5
= 36 km/hr
Therefore, the average speed of the train is 36 km/hr.