The boat covered 12 km upstream and 5 km downstream. In doing so, he spent as much time as it

The boat covered 12 km upstream and 5 km downstream. In doing so, he spent as much time as it would take him if he walked 18 km along the lake. What is the proper speed of the boat, if it is known that the speed of the river flow is 3 km / h.

If we take the speed of the boat as x, then its speed downstream will be:

x + 3 km / h

Against the current, the speed will be:

x – 3 km / h

In this case, the time spent on a walk along the lake will be:

t = s / v = 18 / x h.

Upstream movement will take time:

t = s / v = 5 / (x + 3) h.

And it will go down the stream of time:

t = s / v = 12 / (x – 3) h.

The travel times along the river and along the lake are equal, therefore:

(5 / (x + 3)) + (12 / (x – 3)) = 18 / x;

(5 * (x – 3) + 12 * (x + 3)) / ((x + 3) * (x – 3)) = 18 / x;

x * (5 * x – 15 + 12 * x + 36) = 18 * (x2 – 9);

x * (17 * x + 21) = 18 * (x2 – 9);

17 * x2 + 21 * x = 18 * x2 – 162;

x2 – 21 * x – 162 = 0;

x2 – (27 – 6) * x – 27 * 6 = 0;

(x + 6) * (x – 27) = 0;

Each of the factors in a product equal to zero can turn out to be zero:

x + 6 = 0;

x = -6;

x – 27 = 0;

x = 27.

The negative root can be dropped.

Answer: the boat has a speed of 27 km / h.