The motor ship goes along the river to its destination 140 km and after stopping returns

The motor ship goes along the river to its destination 140 km and after stopping returns to the point of departure. Find the speed of the ship in still water, if the current speed is 5 km / h, the stay lasts 11 hours, and the ship returns to the point of departure 32 hours after leaving it.

Let x be the required value
32 – 11 = 21 hours motor ship en route
Time = distance / speed
140 / (x + 5) – time spent on the way downstream.
140 / (x – 5) – upstream.
(140 / (x + 5)) + (140 / (x – 5)) = 21
Bring to a common denominator (x + 5) (x – 5)
In the numerator of the fraction 140x – 140 * 5 + 140x + 140 * 5 = 280x
The equation is: (280x) / (x + 5) (x – 5) = 21
280x = 21×2 – 525
21×2 – 525 – 280x = 0
Find roots 15 and -10/6 through the discriminant (does not fit)
Hence, x = 15
Answer: 15 km / h



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