The distance between the two marinas, which is equal to 72 km, the motor boat passes the current

The distance between the two marinas, which is equal to 72 km, the motor boat passes the current 2 hours faster than against the current. Find the current speed if the boat’s own speed is 15 km per hour.

The unknown river speed is denoted by x km / h. Then the speed downstream of the river is (15 + x) km / h, and the speed upstream is (15 – x) km / h. Let’s write down the time spent in both directions:
72 / (15 + x) (h) – time of movement along the river;
72 / (15 – x) (h) – time of movement against the stream of the river.
According to the condition of the problem, the time of movement downstream is 2 hours less, we make the equation:
72 / (15 – x) – 72 / (15 + x) = 2
1080 + 72x – 1080 + 72x = 450 – 2x²
2x² + 144x – 450 = 0
x² + 72x – 225 = 0
D = 6084, D> 0, two roots.
x1 = 3;
x2 = – 75 – extraneous root.
Answer: the speed of the current is 3 km / h.