Single correct option
Two cars start at the same time from towns P and Q, 420 km apart, and drive towards each other at constant speeds. They meet after 4 hours. The car from P reaches Q exactly 3 hours after the meeting. What is the speed (in km/h) of the car that started from Q?
- A. 40
- B. 45
- C. 50
- D. 52.5
Show answer and solution
Answer: (B) 45
Let speeds be a (from P) and b (from Q). They meet after 4 h, so a + b = 420/4 = 105.
After meeting, car P covers the stretch car Q had covered before meeting: 3a = 4b → a : b = 4 : 3.
So b = 105 × 3/7 = 45 km/h (and a = 60 km/h).
Check: 60 × 3 = 180 = 45 × 4. ✓
Tip: If t is the meeting time and t₁, t₂ are the times taken after meeting, then t² = t₁t₂ and a : b = √t₂ : √t₁. Here t₂ = 16/3 h.
After meeting, car P covers the stretch car Q had covered before meeting: 3a = 4b → a : b = 4 : 3.
So b = 105 × 3/7 = 45 km/h (and a = 60 km/h).
Check: 60 × 3 = 180 = 45 × 4. ✓
Tip: If t is the meeting time and t₁, t₂ are the times taken after meeting, then t² = t₁t₂ and a : b = √t₂ : √t₁. Here t₂ = 16/3 h.
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