A person moving over a straight path speed v1 for half of the time. fir half of the remaining distance is speed is v2 and for other half v3. find the average speed of tje person?

Question

A person moving over a straight path speed v1  for half of the time.  fir half of the remaining distance is speed is v2 and for other half v3. find the average speed of tje person?

Answer

Problem:

A person moving over a straight path speed v1 for half of the time. For half of the remaining distance, his speed is v2 and for the other half, his speed is v3. Find the average speed of the person?

Solution:

Let's assume the total distance travelled by the person is 'd'.

Time taken to travel the first half of the distance = d/2v1

Distance left to travel = d/2

Time taken to travel the second half of the remaining distance = (d/2v2) * (d/2)

Time taken to travel the second half of the total distance = (d/2v3) * (d/2)

Total time taken = d/2v1 + (d/2v2) * (d/2) + (d/2v3) * (d/2)

Average speed = Total distance / Total time taken = d / (d/2v1 + (d/2v2) * (d/2) + (d/2v3) * (d/2))

Simplifying the above equation:

Average speed = 2v1v2v3 / (v1v2 + v2v3 + v3v1)

Therefore, the average speed of the person is 2v1v2v3 / (v1v2 + v2v3 + v3v1).

Explanation:

In this problem, we were given the speeds of the person for different distances. We first calculated the time taken by the person to travel different distances. Then, we added all the times to get the total time taken by the person to travel the entire distance. Finally, we divided the total distance by the total time to get the average speed of the person. We simplified the equation to get the final answer.

It is important to note that the average speed is not the same as the average of the speeds. We used the formula for the average speed in this problem.

Answer

3÷( (1÷v1)+(1÷v2)+(1÷v3) )

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