The distance between quays A and B is 126 km. The raft sailed from point A along the current

| May 6, 2021 | education

The distance between quays A and B is 126 km. The raft sailed from point A along the current, and an hour later a motor boat set off after it, which, having reached point B, immediately returned back. During this time, the raft sailed 36 km. What is the own speed of the motor boat if the current speed is 4 km / h.

1. The distance between quays A and B is equal to: S = 126 km;

2. Distance that the raft sailed: Sn = 36 km;

3. River flow speed: Vp = 4 km / h;

4. Swimming time of the raft: Tn = Sn / Vp = 36/4 = 9 hours;

5. The sailing time of the motor boat: Tm = Tn – 1 = 9 – 1 = 8 hours;

6. We compose the equation of motion of the boat:

Tno + Tnp = Tm;

S / (Vc + Vp) + S / (Vc – Vp) = Tm;

126 / (Vc + 4) + 126 / (Vc – 4) = 8;

252 * Vc = 8 * (Vc² – 16);

Vc² – 31.5 * Vc – 16 = 0;

Vc1.2 = 15.75 + – sqrt (15.75² + 16) = 15.75 + – 16.25;

A negative root is meaningless;

Vc = 15.75 + 16.25 = 32 km / h.

Answer: the own speed of the motor boat is 32 km / h.



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