The boat at 12:30 left point A to point B, located 30 km from A. After reaching point B for 160 minutes

The boat at 12:30 left point A to point B, located 30 km from A. After reaching point B for 160 minutes, the boat went back and returned to point A at 20:30. Determine (in km / h) the boat’s own speed if the river speed is 3 km / h.

Let the boat’s own speed or 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, since the speed river flow 3 km / h. From the condition of the problem it is known that the boat left point A to point B, located 30 km from A, which means that it will spend 30: (x + 3) hours on the way along the river and 30: (x – 3) hours on path upstream of the river. The boat left at 12:30 from point A to point B, stayed at point B for 160 minutes = 2 (2/3) hours, then the boat went back and returned to point A at 20:30, so it was on the way: 20 , 5 – 12.5 – 2 (2/3) = 5 (1/3) hours.
Knowing this, we compose the equation:
30: (x – 3) + 30: (x – 3) = 5 (1/3);
we will simplify the fractional-rational equation by bringing 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 – 11.25 ∙ x – 9 = 0;
we will solve the quadratic equation, for this we will find the discriminant D = 162.5625;
x₁ = – 0.75 – does not satisfy the condition of the problem;
х₂ = 12 (km / h) – own speed of the boat.
Answer: the boat’s own speed is 12 km / h.