From point A and B, two boats sailed towards each other at the same time. The speed of the river is 3 km / h

From point A and B, two boats sailed towards each other at the same time. The speed of the river is 3 km / h. Having reached point B, the first boat turned around and sailed to point A, simultaneously with the second boat. Find the first boat’s own speed if it is 2 km / h higher than the second boat’s own speed.

1. The speed of the river is equal to: Vр = 3 km / h;

2. Speed ​​of the first boat: V1 km / h;

3. Speed ​​of the second boat: V2 km / h;

4. By the condition of the problem: V1 = V2 + 2 or V2 = V1 – 2 km / h;

5. The second boat was sailing against the current (intuition suggests that the given difference in boat speeds is less than the speed of the river, you can get a negative number under the square root when sailing with the current;

6. Sailing time of the second boat: T2 hour;

T2 = S / (V2 – Vp) = S / ((V1 – 2) – 3) = S / (V1 – 5) hour;

7, The first boat sailed: T1 hour;

T1 = Tpo + Tpro = S / (V1 + Vp) + S / (V1 – Vp) = S / (V1 + 3) + S / (V1 – 3) hour;

8. By the condition of the problem:

T1 = T2;

S / (V1 + 3) + S / (V1 – 3) = S / (V1 – 5);

9. Divide by (S> 0) ^

1 / V1 + 3) + 1 / (V1 – 3) = 1 / (V1 – 5);

(V1 – 3 + V1 +3) / (V1 ^ 2 – 3 ^ 2) = 1 / (V1 – 5);

(2 * V1) / (V1 ^ 2 – 9) = 1 / (V1 – 5);

(2 * V1) * (V1 – 5) = (V1 ^ 2 – 9);

V1 ^ 2 – 10 * V1 + 9 = 0;

V11.2 = 5 + – sqrt (5 ^ 2 – 9) = 5 + – 4;

V1 = 5 – 4 = 1 km / h (does not satisfy the conditions of the problem, since V1 <Vр);

V1 = 5 + 4 = 9 km / h.

Answer: the speed of the first boat is 9 km / h.