The boat set off at 15 o’clock. I walked 7 km upstream and stopped for 2 hours. After that, he went another 27 km

The boat set off at 15 o’clock. I walked 7 km upstream and stopped for 2 hours. After that, he went another 27 km downstream and arrived at the point at 19 o’clock. Find your own speed of the boat if the current speed is 2 km / h.

The time from the departure of the boat to the arrival at the final destination was 19 – 15 = 4 hours.

But since the boat made a stop for 2 hours, it means that it was only 4 – 2 = 2 hours on the way.

Let’s say the speed of the boat is x km / h, then it floats against the current at a speed

(x – 2) km / h, and downstream at a speed of (x + 2) km / h.

Therefore, the boat will cover 7 km upstream in 7 / (x – 2) hours, and 27 km downstream –

in 27 / (x + 2) hours. We get the equation:

7 / (x – 2) + 27 / (x + 2) = 2,

7 * x + 14 + 27 * x – 54 = 2 * (x + 2) * (x – 2),

34 * x – 40 = 2 * x² – 8,

2 * x² – 34 * x + 32 = 0,

x² – 17 * x + 16 = 0.

Let’s find the discriminant of this equation:

D = 17² – 4 * 1 * 16 = 289 – 64 = 225.

x = (17 – 15) / 2 = 1 and x = (17 + 15) / 2 = 16.

Since the speed of the boat cannot be less than the current speed of 2 km / h (the boat will demolish), then the speed of the boat is 16 km / h.

Answer: 16 km / h.