The boat traveled 36 km along the river and returned back for 5 hours. The speed of the river is 3 km / h.

The boat traveled 36 km along the river and returned back for 5 hours. The speed of the river is 3 km / h. Find the speed of the boat.

We form an equation with one unknown, in which we denote the own speed of the boat as the unknown number x.

Thus, the boat was going downstream at a speed of x + 3 km / h, and against it at a speed of x – 3 km / h.

36 / (x + 3) + 36 / (x – 3) = 5 hours.

36 * (x – 3) + 36 * (x + 3) = 5 * (x + 3) * (x – 3).

36 * x – 108 + 36 * x + 108 = 5 * (x ^ 2 – 3 * x + 3 * x – 9).

72 * x = 5 * x ^ 2 – 45.

5 * x ^ 2 – 72 * x – 45 = 0.

D ^ 2 = (-72) ^ 2 – 4 * 5 * (-45) = 5184 + 900 = 6084.

D = √6084 = 78.

x = (72 + 78) / 5 * 2 = 150/10 = 15 km / h.

Answer: 15 km / h.