The motor boat passed against the current for 24 km and returned back, spending 20 minutes less on

The motor boat passed against the current for 24 km and returned back, spending 20 minutes less on the way back than when moving against the current. Find the speed (in km / h) of the boat in still water if the current speed is 3 km / h.

Solution.
Let the own speed of a motor boat, or the speed in still water be x km / h, then the speed of the boat along the river will be (x + 3) km / h, and the speed of the boat against the river will be (x – 3) km / h, so as the speed of the river is 3 km / h. From the condition of the problem it is known that the motor boat passed against the stream of the river 24 km in 24: (x – 3) hours and returned back in 24: (x + 3) hours, having spent 20 minutes = 1/3 hour less on the way back, than when moving against the current. Knowing this, we compose the equation:
24: (x – 3) – 24: (x + 3) = 1/3;
we will simplify the fractional-rational equation by reducing its terms to a common denominator, and multiplying both sides of the equation by a common denominator (x² – 9);
after reducing similar terms, we get:
x² – 441 = 0;
we solve the quadratic equation:
x₁ = – 21 (km / h) – does not satisfy the condition of the problem;
x₂ = 21 (km / h) – the boat’s own speed.
Answer: the speed of the boat in still water is 21 km / h.