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.