The motor boat passed 16 km against the river flow and returned back, spending 45 minutes less on the way

The motor boat passed 16 km against the river flow and returned back, spending 45 minutes less on the way back than on the way upstream. The speed of the river is two kilometers per hour. Find the speed of the boat in still water.

Answer: Let us denote by x – the boat’s own speed (in still water).

Then, the speed of the boat downstream – (x + 2), and against the current (x – 2).

Let’s make the equation:

16 / (x – 2) – 16 / (x + 2) = 1. We multiply both sides of the equation by (x – 2) * (x + 2), then

16 * (x + 2) – 16 * (x – 2) = (x – 2) * (x + 2). Let’s expand the brackets and present similar terms.

x ^ 2 – 4 = 64; x ^ 2 = 68; x = ± √68.

Since the speed is a positive value x = 2√17 (km / h).
Answer: 2√17 km / h.