Single correct option
Two cars A and B start at the same time from towns P and Q respectively, 300 km apart, and drive towards each other at constant speeds. After they meet, A takes 4 more hours to reach Q and B takes 9 more hours to reach P. What is the speed of car A (in km/h)?
- A. 30
- B. 36
- C. 25
- D. 20
Show answer and solution
Answer: (A) 30
Let them meet after t hours. The distance B covered before the meeting (B's speed × t) is what A covers in 4 h afterwards, and vice versa:
vB·t = 4·vA and vA·t = 9·vB.
Multiplying: t² = 36, so t = 6 h. Dividing: (vA/vB)² = 9/4, so vA : vB = 3 : 2.
A covers the full 300 km in 6 + 4 = 10 h, so vA = 30 km/h (and vB = 300/15 = 20 km/h). Check: in 6 h they close 6 × 50 = 300 km ✓.
Shortcut: meeting time = √(t₁t₂) and speed ratio = √(t₂/t₁).
vB·t = 4·vA and vA·t = 9·vB.
Multiplying: t² = 36, so t = 6 h. Dividing: (vA/vB)² = 9/4, so vA : vB = 3 : 2.
A covers the full 300 km in 6 + 4 = 10 h, so vA = 30 km/h (and vB = 300/15 = 20 km/h). Check: in 6 h they close 6 × 50 = 300 km ✓.
Shortcut: meeting time = √(t₁t₂) and speed ratio = √(t₂/t₁).
Saved on this device. Sign in or create a free account to keep it on every device.