a boy walks to a school at a rate of 6km with a speed of 2.5km/h and walks back with a constant speed of 5km/h. his average speed for round trip in km/h is ?
You must mean that the rate of walking to school is 6 km/h, not 6 km.
Let the distance to school be D. (It will cancel out when you compute the avg. speed)
avg speed = (total distance covered)/(total time)
= 2D/[D/6 + D/2.5}
= 2/[(1/6 + 4/10]
= 2/[5/30 + 12/30]
= 60/17 = 3.53 km/h
Note that this is NOT the average of 6 and 2.5. He spends more time walking at the lower speed.
To find the average speed for a round trip, we need to find the total distance and the total time taken.
The distance to the school is 6km, and the boy walks with a speed of 2.5km/h. Therefore, the time taken to reach the school is obtained by dividing the distance by the speed: 6km / 2.5km/h = 2.4 hours.
On the way back, the boy walks with a speed of 5km/h. The distance remains the same (6km), so the time taken to return is obtained by dividing the distance by the speed: 6km / 5km/h = 1.2 hours.
Now, we can calculate the total time taken for the round trip by summing the time taken to go to the school and the time taken to return: 2.4 hours + 1.2 hours = 3.6 hours.
The total distance for the round trip is twice the distance to the school, since the boy travels the same distance twice: 2 * 6km = 12km.
Finally, we can find the average speed by dividing the total distance by the total time taken: 12km / 3.6 hours = 3.33 km/h.
Therefore, the average speed for the round trip is 3.33 km/h.