Problem 86.

A body covers 1/4 journey with a speed of 40 km/h, 1/2 of it with 50 km/h and remaining with the speed of 60 km/h. Calculate average speed for entire journey.

Solution:

In this problem we need to use the definition of the average speed. The average speed is equal to the ratio of the total travelled distance and the total traveled time:

We introduce the total traveled distance as and then calculate the total traveled time.

We know that 1/4 of the journey a body moves with a speed of 40 km/h. It means that the body moves a distance of with the speed of 40 km/h. Then we can find the time of this motion:

Then the body moves 1/2 of the journey with a speed of 50 km/h. It means that the body moves a distance of with the speed of 50 km/h. We can find the time of this motion:

Then the body moves the rest of the journey (which is 1/4 of the journey) with a speed of 60 km/h. It means that the body moves a distance of with the speed of 60 km/h. We can find the time of this motion:

Then the total traveled time is

Then the average speed is