The distance between the two marinas is 60 km. The motor ship travels this distance upstream and upstream in 5.5 hours.

The distance between the two marinas is 60 km. The motor ship travels this distance upstream and upstream in 5.5 hours. Find the speed of the ship in still water and the speed of the current if one of them is 20 km / h more than the other.

1) Let x km / h be the speed of the river, then (x + 20) km / h is the speed of the ship in still water (its own speed).
2) To find the speed of the ship along the river, you need to add the speed of the river to its own speed:
(x + 20) + x = 2x + 20 (km / h) – the speed of the ship along the river.
3) To find the speed of the motor ship against the river flow, you need to reduce its own speed by the speed of the river flow:
(x + 20) – x = 20 km / h – speed of the ship against the river flow.
4) Then 60 / (2x + 20) hours is the time of movement of the ship along the river,
60/20 = 3 hours – upstream of the river.
5) Since the motor ship spent 5.5 hours for the entire journey, it is possible to determine the time it took to travel along the river:
5.5 – 3 = 2.5 hours.
6) You can write equality:
60 / (2x + 20) = 2.5.
7) We solve the composed equation:
60 = 2.5 * (2x + 20),
60 = 2.5 * 2x + 2.5 * 20,
60 = 5x + 50,
60 – 50 = 5x,
10 = 5x,
x = 2.
8) Having solved the equation, we find that the speed of the river flow x = 2 km / h.
9) Let’s calculate the speed of the ship in still water:
2 + 20 = 22 km / h.
Answer: 22 km / h is the speed of the ship in still water, 2 km / h is the speed of the river.