The boat traveled 15 km upstream and 6 km downstream, spending the same amount of time as it would

The boat traveled 15 km upstream and 6 km downstream, spending the same amount of time as it would have taken if it had walked 221 across the lake. What is the boat’s own speed if it is known that the speed of the river is 2 km / h?

The speed of the boat will be designated as “a” km / h.

Taking into account the condition of the problem, we compose the equation:

15 / (a – 2) + 6 / (a + 2) = 22a;

(15а + 30) / (а² + 2а – 2а – 4) + (6а – 12) / (а² + 2а – 2а – 4) = 22 / а;

(15а + 30 + 6а – 12) / (а² – 4) = 22 / а;

(21a + 18) / (a² – 4) = 22 / a;

21a + 18 = 22 / a * (a² – 4);

21a + 18 = 22a – 88 / a;

21а² + 18а = 22а² – 88;

-а² + 18а + 88 = 0;

a = (-18 – √ (18² – 4 * (-1) * 88)) / (- 2);

a = (-18 – √ (324 + 352)) / (- 2);

a = (-18 – 26) / (- 2);

a = (-44) / (- 2);

a = 22 km / h, own speed of the boat.