There are quays A, B and C downstream of the river. Distance AB = 12 km, BC = 8 km. The boat, starting from A

There are quays A, B and C downstream of the river. Distance AB = 12 km, BC = 8 km. The boat, starting from A, reached C and, turning back, arrived at B, spending an hour and a half for the entire journey. Then the boat went to A and immediately returned to B, spending 1 hour 21 minutes on this route. What is the boat’s own speed and the speed of the river flow?

Let’s take the speed of the boat and the current as k and t (km / h), the speed along and against the current – (k + t), and (k – t).

1) 12 / (k + t) + 12 / (k – t) = 1 21/60 = 1.35,

2) (12 + 8) / k + t) + 8 / (k – t) = 1.5;

12 * k + 12 * k = 1.35 * (k ^ 2 – m ^ 2);

20 * k – 20 * t + 8 * k – 8 * t = 1.5 (k ^ 2 – m ^ 2);

1) 24 * k = 1.35 * (k ^ 2 – m ^ 2), (* 1.5); 2) 28 * k – 12 * m = 1.5 * (k ^ 2 – m ^ 2), (* 1.35).

(37.8 * k – 16.2m = 36 * k, whence 1.8 * k = 16.2 * t, k = 9 * t.

20 / (9t + t) + 8 / (9 * t – t) = 1.5; 20 / 10t + 8 / 8t = 1.5; 2 / t + 1 / t = 1.5; 3 / t = 1.5, t = 2, k = 18 (km / h).