Single correct option
A and B start at the same time from towns P and Q respectively and travel towards each other. After they meet, A takes 16 hours to reach Q and B takes 9 hours to reach P. If A's speed is 36 km/h, what is B's speed?
- A. 27 km/h
- B. 42 km/h
- C. 48 km/h
- D. 64 km/h
Show answer and solution
Answer: (C) 48 km/h
Let them meet after t hours. The distance A covers after the meeting (16·vA) equals what B covered before it (t·vB), and similarly 9·vB = t·vA.
Dividing: 16vA/(9vB) = vB/vA, so (vA/vB)² = 9/16 and vA/vB = 3/4.
vB = 36 × 4/3 = 48 km/h.
Shortcut: vA : vB = √(tB) : √(tA), where tA, tB are the times after meeting.
Dividing: 16vA/(9vB) = vB/vA, so (vA/vB)² = 9/16 and vA/vB = 3/4.
vB = 36 × 4/3 = 48 km/h.
Shortcut: vA : vB = √(tB) : √(tA), where tA, tB are the times after meeting.
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