The boat went down along the river, having covered 28 km, and immediately returned back

| December 28, 2020 | education

The boat went down along the river, having covered 28 km, and immediately returned back, spending 7 hours for the entire journey. What is the speed of the boat in still water if the river speed is 3 km / h?

Let the boat’s own speed be x km / h. Then the time he walked downstream was 28 / (x + 3) hours.
On the road against the stream of the river, the speed will be equal to (x – 3) km / h, the time spent on this path is 28 / (x – 3) hours. If the whole journey took 7 hours, the equation will look like:
28 / (x + 3) + 28 / (x-3) = 7,
28 (x – 3) + 28 (x + 3) = 7 (x – 3) (x + 3),
28x – 84 + 28x + 84 = 7 x2 – 63,
7 x^2 – 56x – 63 = 0,
x^2 – 8x – 9 = 0,
D = b^2 – 4ac
D = 64 – 4 * (-9) = 64 + 36 = 100.
x = (-b ± √D) / 2a
x = 8 ± 10/2
x1 = 9, x2 = -1.
But x2 = -1 is not a solution to the problem, because speed cannot be less than zero.
Answer: the speed of the boat in still water is 9 km / h.



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