The motor boat traveled 48 km downstream and 70 km upstream, spending 1 hour less downstream

The motor boat traveled 48 km downstream and 70 km upstream, spending 1 hour less downstream than upstream. Find your own boat speed if the river speed is 2 km / h

Let the speed of the motor boat in still water, or the boat’s own speed, be X km / h. According to the condition, the speed of the river flow is 2 km / h, then the speed of the boat moving against the flow of the river will be (X – 2) km / h, and the speed of the boat moving along the river will be (X + 2) km / h. The motor boat passed 48 km downstream, spending 48: (X + 2) hours on the way. She covered 70 km upstream, spending 70: (X – 2) hours on the way. Knowing that 1 hour less was spent on the way downstream than on the way upstream, we compose the equation:
48: (X + 2) + 1 = 70: (X – 2).
We got a fractional rational equation, simplifying which, we come to a quadratic equation:
X² – 22 ∙ X – 240 = 0; solve it, discriminant D = 1444,
root X1 = – 8 – does not satisfy the condition of the problem;
X2 = 30 (km / h) – the boat’s own speed.
Answer: the boat’s own speed is 30 km / h.