# 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.