# The boat sails the distance between two villages in 4 hours upstream and 6 hours upstream.

**The boat sails the distance between two villages in 4 hours upstream and 6 hours upstream. Find the speed of the boat and the current of the river if the distance between the villages is 60 km.**

1. Let’s designate the speed of the boat through X km / h, and the speed of the river through Y km / h.

2. Then, when moving along the river, the boat relative to the coast will have a speed

(X + Y) km / h. That is, we get equality: (X + Y) * 4 = 60.

3. When moving against the stream of the river, the boat relative to the bank will have a speed

(X – Y) km / h. That is, we get equality: (X – Y) * 6 = 60.

4. Divide both sides of the first equation by 4, and both sides of the second by 6. We obtain a system of two equations:

X + Y = 15

X – Y = 10.

5. We add these equations and divide both sides of the resulting equality by 2.

We get: X = 12.5 km / h.

6. From the first equation Y = 15 – 12.5 = 2.5 km / h.

Answer: the speed of the boat is 12.5 km / h, the speed of the river is 2.5 km / h.