Numerical answer
Two cyclists A and B start at the same time from towns P and Q respectively and ride towards each other at constant speeds. After they meet, A takes 16 hours more to reach Q and B takes 9 hours more to reach P. If A rides at 30 km/h, what is the distance (in km) between P and Q?
Show answer and solution
Answer: 840
Standard result: if after meeting the two take t₁ and t₂ hours, then vA/vB = √(t₂/t₁) and the time to meet t = √(t₁t₂).
Why: before meeting, A covers what B covers after meeting: vA·t = vB·9 and vB·t = vA·16. Multiply: t² = 144 → t = 12 h; divide: (vA/vB)² = 9/16 → vA/vB = 3/4.
So vB = 40 km/h and PQ = (30 + 40) × 12 = 840 km.
Why: before meeting, A covers what B covers after meeting: vA·t = vB·9 and vB·t = vA·16. Multiply: t² = 144 → t = 12 h; divide: (vA/vB)² = 9/16 → vA/vB = 3/4.
So vB = 40 km/h and PQ = (30 + 40) × 12 = 840 km.
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