From two points of the river, two motor boats left at the same time towards each other.

| February 2, 2021 | education

From two points of the river, two motor boats left at the same time towards each other. After 1.2 hours they met. The own speed of the boat, which was going along the river, is 18 km / h, and the boat, which was going against the river, 16 km / h. Before the meeting, one boat passed 9.6 km more than the other. Find the speed of the river and the distance each boat traveled before the meeting.

Let the speed of the river flow x km / h. Then the speed of the first boat downstream is (18 + x) km / h, and the speed of the second boat against the river is (16) km / h.
Then the first boat passed 1.2 (18 + x), the second boat passed 1.2 (16). According to the condition, the first boat passed 9.6 km more than the other. I.e:
1.2 (18 + x) -1.2 (16-x) = 9.6.
21.6 + 1.2x-19.2 + 1.2x = 9.6.
1.2x + 1.2x = 9.6-21.6 + 19.2.
2.4x = 7.2.
x = 7.2: 2.4.
x = 3.
For x we ​​took the speed of the river.
Let’s calculate the speed of the first boat:
1) 18 km / h + 3 km / h = 21 km / h.
Let’s calculate the distance that the first boat covered before the meeting:
2) 21 km / h * 1.2 h = 25.2 km.
Let’s calculate the speed of the second boat:
3) 16 km / h – 3 km / h = 13 km / h.
Let’s calculate the distance that the second boat traveled before the meeting:
4) 13 km / h * 1.2 h = 15.6 km.
Answer: the speed of the river is 3 km / h. The first boat passed 25.2 km before the meeting. The second boat passed 15.6 km to the meeting.



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