The traveler climbed the mountain at a speed of 3 km / h and then descended back

The traveler climbed the mountain at a speed of 3 km / h and then descended back at a speed of 6 km / h. what is the average speed of the traveler along the way?

Given:

v1 = 3 km / h – the speed of the traveler when going uphill;

v2 = 6 km / h – the speed of the traveler when descending the mountain.

It is required to determine v (km / h) – the average speed of the traveler along the entire journey.

Let S be the distance from the foot to the top of the mountain. Then the entire distance traveled will be equal to 2 * S.

The time for climbing the mountain is:

t1 = S / v1.

Descent time from the mountain is:

t2 = S / v2.

The total travel time is:

t = t1 + t2 = / v1 + S / v2 = S * (v1 + v2) / * v1 * v2).

The average speed will be equal to:

v = 2 * S / t = 2 * S / (S * (v1 + v2) / * v1 * v2)) = 2 * v1 * v2 / (v1 + v2) =

= 2 * 3 * 6 / (3 + 6) = 36/9 = 4 km / h.

Answer: the average speed of a traveler is 4 km / h.