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.
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