# The motor ship travels the distance from pier A to pier B, located downstream, in 30 minutes.

**The motor ship travels the distance from pier A to pier B, located downstream, in 30 minutes. The raft covers the same distance in 2.5 hours. Find the time of return of the ship from B to A.**

Given:

t1 = 30 minutes – the time during which the ship passes the distance from point A to point B, moving along the river;

t2 = 2.5 hours = 150 minutes – the time during which the raft travels the distance from point A to point B, moving along the river.

It is required to determine t3 (minutes) – the time during which the ship will return from point B to point A.

Let S be the distance from point A to point B.

Then, the speed of the river will be equal to:

v = S / t2.

The speed of the ship will be equal to:

S / (v1 + v) = t1;

S = v1 * t1 + v * t1;

v1 = (S – v * t1) / t1 = (S – S * t1 / t2) / t1 = S * (t2 – t1) / (t1 * t2).

The relative speed of the ship against the river flow is equal to:

v2 = v1 – v = S * (t2 – t1) / (t1 * t2) – S / t2 = S * (t2 – 2 * t1) / (t1 * t2).

Then:

t3 = S / v2 = S / (S * (t2 – 2 * t1) / (t1 * t2)) = t1 * t2 / (t2 – 2 * t1) =

= 30 * 150 / (150 – 2 * 30) = 4500/90 = 50 minutes.

Answer: the ship will return in 50 minutes.