The distance between quays A and B is 75 km. A raft departed from A to B along the river, and an hour

| June 28, 2021 | education

The distance between quays A and B is 75 km. A raft departed from A to B along the river, and an hour later a motor boat set off after it, which, having arrived at point B, immediately turned back and returned to A. By this time, the raft had covered 44 km. Find the speed of the boat in still water if the speed of the river is 4 km / h.

If the raft covered 44 km at a speed of 4 km / h (the speed of the raft coincides with the speed of the current), then it spent 11 hours, the boat 10 hours. Let’s take the boat’s own speed as x km / h. Then the speed downstream is (x + 4) km / h, and against – (x-4) km / h.
Time downstream – 75 / (x + 4) h, and against – 75 / (x-4) h.
75 / (x + 4) + 75 / (x-4) = 10
Let’s bring the left side to a common denominator:
150x / (x ^ 2 -16) = 10 Reduce the equation by 10 and write:
x ^ 2 -15x -16 = 0
x1 + x2 = 15
x1 * x2 = 16
x1 = 16
x2 = -1 (not satisfied)
Answer. 16km / h



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