Answer :

Let speed of boat in still water be x km/hr.

∵ speed of river is given as 1 km/hr

⇒ speed of boat downstream = (x + 1) km/hr.

∴ let time taken to go 112 km downstream = t

Now, speed of boat upstream will be (x – 1) km/hr.

∴ let time taken to go 112 km upstream = T

Given that total journey time was 15 hr

⇒ t + T = 15

⇒ 112x – 112 + 112x + 112 = 15x^{2} – 15

⇒ 15x^{2} – 224x – 15 = 0

⇒ 15x^{2} – 224x – 15 = 0

⇒ 15x^{2} – (225 – 1)x – 15 = 0

⇒ 15x^{2} – 225x + x – 15 = 0

⇒ 15x(x – 15) + 1(x – 15) = 0

o r

And speed cannot be negative.

⇒ x = 15 km/hr.

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