The distance between two points, the boat sails downstream in 4 hours, and against the current in 5 hours

| September 2, 2021 | education

The distance between two points, the boat sails downstream in 4 hours, and against the current in 5 hours, how many hours the raft will sail between the same points.

Let x km / h be the speed of the boat, and um / h the speed of the river flow (speed of the raft). Then the speed of the boat along the river is (x + y) km / h. and upstream of the river (x – y) km / h. Let’s take the entire path as a unit. We know that the boat travels downstream for this distance in 4 hours, and against the current in 5 hours. We compose a system of equations: the system 1 / (x + y) = 4 and 1 / (x – y) = 5; system: x + y = 1/4, x – y = 1/5 from the second equation of the system we express x and substitute it into the first equation and we get the system: x = 1/5 + y, 1/5 + y + y = 1 / 4; multiply the second equation of the system by 20 and get the system: x = 1/5 + y, 4 + 40y = 5; system x = 1/5 + y, 40y = 1; system x = 1/5 + y, y = 1/40 km / h. Let’s find the time for which the raft will sail this distance. 1: 1/40 = 40 (h.)
Answer: in 40 hours.



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