The boat traveled in 4 hours against the current of the river a route 9.5 km longer than the route

The boat traveled in 4 hours against the current of the river a route 9.5 km longer than the route in 2.5 hours downstream. Find your own boat speed if the current speed is 2 km / h.

Let the boat’s own speed be x km / h. Then the speed of the boat against the current is equal to:

x – 2 km / h;

The speed of the boat downstream is:

x + 2 km / h.

The path of the boat against the current for 4 hours was:

4 * (x – 2) = 4 * x – 8 km.

The path of the boat downstream for 2.5 hours was:

2.5 * (x + 2) = 2.5 * x + 5 km.

Moreover, the difference between these distances is 9.5 km:

4 * x – 8 – (2.5 * x + 5) = 9.5;

4 * x – 8 – 2.5 * x – 5 = 9.5;

1.5 * x – 13 = 9.5;

1.5 * x = 9.5 + 13 = 22.5;

x = 22.5 / 1.5 = 15.

Answer: the boat’s own speed is 15 km / h.