Two cars, X and Y, start from points 360 km apart and travel at constant speeds. If they move towards each other, they meet in 4…

Question

Two cars, X and Y, start from points 360 km apart and travel at constant speeds. If they move towards each other, they meet in 4 hours. If they move in the same direction, they meet in 12 hours. What is the speed of car X? (Assume X is the faster car).

1. A. 60 km/h (Correct answer)
2. B. 75 km/h
3. C. 45 km/h
4. D. 90 km/h

Correct Answer

Option A — 60 km/h

Detailed Solution & Explanation

The correct answer is 60 km/h.

Key Points

• Moving toward each other, combined speed = 360/4 = 90 km/h, so x + y = 90. Moving the same way, the gap closes at the speed difference = 360/12 = 30 km/h, so x − y = 30. Adding the equations: 2x = 120 → x = 60 km/h (and y = 30).
• Opposite directions add speeds, same direction subtracts them — set up the sum and difference, then solve the pair.