A train travels some distance with the speed of 30 km/h and returns with the speed of 45km/h. Calculate the average speed of the train
To calculate the average speed of the train, we need to use the formula:
Average Speed = Total Distance / Total Time
First, we need to find the total distance covered by the train.
Let's assume the distance covered by the train in one direction is 'D' km.
In the first case, the train is moving at a speed of 30 km/h. So, the time taken to cover the distance 'D' would be:
Time taken = Distance / Speed = D / 30
In the second case, the train is moving at a speed of 45 km/h. So, the time taken to cover the same distance 'D' would be:
Time taken = Distance / Speed = D / 45
Now, to find the total distance covered by the train, we can simply add the distances traveled in both directions:
Total Distance = D + D = 2D
Next, let's calculate the total time taken by the train for the round trip. The round trip consists of going from one point to another and then returning back. Therefore, the total time taken would be the sum of the time taken in both directions:
Total Time = (D / 30) + (D / 45)
Now, let's substitute the values of total distance and total time into the average speed formula:
Average Speed = Total Distance / Total Time
Average Speed = 2D / [(D / 30) + (D / 45)]
We can simplify this equation further by finding the common denominator:
Average Speed = 2D / [(3D + 2D) / (90)]
Average Speed = 2D * (90 / 5D)
Average Speed = 180 / 5
Average Speed = 36 km/h
Therefore, the average speed of the train is 36 km/h.
use 45 km as the distance
the train travels 90 km in 2.5 hr