# The boat covered 87.5 km along the river in 5 hours, and against the current the same

The boat covered 87.5 km along the river in 5 hours, and against the current the same distance in 7 hours. What is the boat’s own speed and the speed of the river flow?

Let’s find the speed of the boat along the river, I know the total number of km and the time: 87.5 / 5 = 17.5 (km / h).
Let’s find the speed of the boat against the stream of the river, I know the total number of km and the time: 87.5 / 7 = 12.5 (km / h).
Let x be the speed of the boat and y the speed of the river.
Then x + y = 17.5 (downstream speed = proper speed + river speed), and x – y = 12.5 (similar to the previous one).
Let us express x through y in the first equation: x = 17.5 – y. Substitute the resulting expression into the second equation: 17.5 – y – y = 12.5. Let’s solve the equation:
17.5 – 12.5 = 2y,
5 = 2y,
y = 2.5 (km / h) – the speed of the river.
Find the boat’s own speed: x = 17.5 – 2.5 = 15 (km / h).

Answer: the speed of the river is 2.5 km / h, and the speed of the boat is 15 km / h.

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