The distance between quays A and B is 108 km. A raft departed from A to B along the river, and an hour later

The distance between quays A and B is 108 km. A raft departed from A to B along the river, and an hour later a motor boat set off after it, which, having arrived at point B, immediately turned back and returned to A. By this time, the raft had covered 48 km. Find the speed of the boat in still water if the river speed is 3 km / h.

The time it took the boat to cover the distance from A to B and back is equal to the travel time of the raft reduced by 1 hour. Let’s calculate:

T = 48/3 – 1 = 16 – 1 = 15 (h).

Let’s designate the speed of the boat along the current “X + 3”, and against the current “X – 3”. Let’s compose and solve the equation:

108 / (X + 3) + 108 / (X – 3) = 15;

(108 * (X – 3) + 108 * (X + 3) – 15 * (X + 3) * (X – 3)) / ((X + 3) * (X – 3)) = 0;

X ≠ -3; X ≠ 3;

108X – 324 + 108X + 324 – 15X ^ 2 + 135 = 0;

–15X ^ 2 + 216X + 135 = 0;

5X ^ 2 – 72X – 45 = 0;

D = 5184 + 900 = 6084;

X1 = (72 – 78) / 10 <0;

X2 = (72 + 78) / 10 = 15 (km / h).

Answer: the speed of the boat in still water is 15 km / h.