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P starts from A at 6 a.111. and reaches B after 8 hours. Q stat1s from B at 8 a.m. and reaches A after 9 hours. When they meet,
what is the ratio of the distance travelled by Q to the distance travelled by P?
3 : 8
6 : 7
6 : 11
8 : 3
- P starts from A at 6 a.m. and takes 8 hours to reach B.
- Hence, P reaches B at 2 p.m.
- Q starts from B at 8 a.m. and takes 9 hours to reach A.
- Therefore, Q reaches A at 5 p.m.
- Let the distance between A and B be D.
- The speed of P = D/8.
- The speed of Q = D/9.
- They meet at some point t hours after P starts at 6 a.m.
- At that moment, the distance P has traveled is (D/8) * t.
- Q traveled for t - 2 hours since Q started at 8 a.m.
- The distance Q has traveled is (D/9) * (t - 2).
- Since they meet at the same point:
- (D/8) * t + (D/9) * (t - 2) = D.
- Solving gives t = 24/5 hours (or 4.8 hours).
- When they meet:
- Distance traveled by P = (D/8) * 4.8 = 0.6D.
- Distance traveled by Q = (D/9) * 2.8 = 0.4D.
- The ratio of the distances: 0.4D : 0.6D simplifies to 2:3.
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