From pier A, a boat and a raft departed downstream of the river. The boat swam to B, turned back

| May 6, 2021 | education

From pier A, a boat and a raft departed downstream of the river. The boat swam to B, turned back and met the raft 4 hours after leaving A. Then the time of boat movement from A to B is equal to?

1. The raft has sailed distance: Sn km;
2. Distance covered by the current: Sno km;
3. Distance, which the boat sailed against the current: Snp km;
4. Own speed of the boat: Vc km / h;
5. The speed of the river is equal to: Vp km / h;
6. Time of sailing the raft before the meeting: T = 4 hours;
7. We make the equation in time:

Tno + Tnp = Tn;
Sno / Vno + Snp / Vnp = 4;
Sno / (Vc + Vp) + (Sno – Vp * Tn) / (Vc – Vp) = 4;
Sno * (Vc – Vp + Vc + Vp) / (Vc² – Vp²) = 4 + Vp * 4 / (Vc – Vp);
2 * Sno * Vc / (Vc² – Vp²) = (4 * Vc – 4 * Vp + 4 * Vp) / (Vc – Vp);
Sno / (Vc² – Vp²) = 2 / (Vc – Vp);
Sno / (Vc + Vp) = 2;
Tno = 2 hours.
Answer: from pier A to B the boat sailed for 2 hours.



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