# The boat covered 36 km along the river and 20 km along the lake, spending 5 hours

The boat covered 36 km along the river and 20 km along the lake, spending 5 hours for the whole journey. Find your own boat speed if the river speed is 2 km / h

Let the boat’s own speed be x km / h, then the speed of the boat along the river is (x + 2) km / h. The boat passed the distance of 36 kilometers along the river in 36 / (x + 2) hours, and on the lake 20 kilometers in 20 / x hours. According to the condition of the problem, it is known that the boat spent (36 / (x + 2) + 20 / x) hours or 5 hours for the entire journey. Let’s make an equation and solve it.

36 / (x + 2) + 20 / x = 5 – the common denominator is x (x + 2); the additional factor for the first fraction is x, for the second fraction is (x + 2), for the third fraction 5 = 5/1 is x (x + 2);

O.D.Z. x ≠ 0, x ≠ -2;

36x + 20 (x + 2) = 5x (x + 2);

36x + 20x + 40 = 5x ^ 2 + 10x;

5x ^ 2 + 10x – 36x – 20x – 40 = 0;

5x ^ 2 – 46x – 40 = 0;

D = b ^ 2 – 4ac;

D = (-46) ^ 2 – 4 * 5 * (-40) = 2916; √D = 54;

x = (-b ± √D) / (2a);

x1 = (46 + 54) / (2 * 5) = 100/10 = 10 (km / h);

x2 = (46 – 54) / 10 = -8/10 – the speed cannot be negative. 