The motor boat sailed against the current for 91 km and returned back. On the way back it took 6 hours less

The motor boat sailed against the current for 91 km and returned back. On the way back it took 6 hours less. Find the speed of the boat in still water if the current speed is 3 km / h.

Let the speed of a motor boat in still water, or its own speed is 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 of the river is 3 kilometers per hour. It is known from the problem statement that the motor boat sailed 91 km against the river and returned back, spending 91: (x + 3) hours on the way along the river and 91: (x – 3) hours on the way against the river. Knowing that she spent 6 hours less on the way back, we make the equation:
91: (x + 3) + 6 = 91: (x – 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 – 100 = 0;
solve the quadratic equation,
x₁ = – 10 – does not satisfy the condition of the problem;
x₂ = 10 (km / h) – the boat’s own speed.
Answer: the boat’s own speed is 10 km / h.