The motor ship sailed 18 km beyond the course of the river and returned back for the entire

| January 2, 2021 | education

The motor ship sailed 18 km beyond the course of the river and returned back for the entire time it spent 1 hour and 45 minutes. Find the speed of the river if the speed of the ship in standing water is 21 km / h.

The speed of the river is denoted by x (in km / h). Then the speed of the motor ship along the river will be (21 + x) km / h, and against the river – (21 – x) km / h.
The time spent by the motor ship to move along the river is 18 / (21 + x) hours, against the river – 18 / (21 – x) hours.
Let’s express 1 hour 45 minutes in hours. Since 1 hour = 60 minutes, then 1 hour 45 minutes = (1 + 45/60) hour = 1.75 hours. According to the conditions of the assignment, we compose and solve the following equation 18 / (21 + x) + 18 / (21 – x) = 1.75.
We have 18 * (21 – x + 21 + x) = 1.75 * (21 – x) * (21 + x) or, using the abbreviated multiplication formula (a – b) * (a + b) = a2 – b2 ( difference of squares), 432 = 441 – x². The last incomplete quadratic equation has two different roots: x = –3 and x = 3.
According to the conditions of the task, x cannot take negative values, that is, x = –3 is a side root. This means that the speed of the river is 3 km / h.
Answer: 3 km / h.



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