A boat runs between points A and B, located on the river bank at a distance

A boat runs between points A and B, located on the river bank at a distance of 100 km. One way – 4 hours, the other – 10 hours. What is the speed of the current?

Given:

L = 100 kilometers – the distance between points A and B;

t1 = 4 hours – the time of boat movement from point A to B along the river;

t2 = 10 hours – time of boat movement from point B to point A against the river flow.

It is required to determine Vр (km / h) – the speed of the river flow.

Let Vk be the speed of the boat, constant when moving back and forth. Then, when moving along the river, the boat moves with a total speed V1 = Vк + Vр, and when moving against the river flow – V2 = Vк – Vр. We get a system of two equalities:

Vк + Vр = L / t1;

Vк – Vр = L / t2.

We subtract the second from the first equality:

Vk + Vp – Vk + Vp = L / t1 – L / t2.

2 * Vp = L * (t2 – t1) / (t1 * t2);

Vp = L * (t2 – t1) / (2 * t1 * t2) = 100 * (10 – 4) / (2 * 10 * 4) =

= 100 * 6/80 = 600/80 = 60/8 = 7.5 km / h.

Answer: the speed of the river is 7.5 km / h.