Two cars A and B leave the same point for the same destination. Speeds are 30 km/h (A) and 45 km/h (B). Car B reaches 2 hours earlier than car A. What is the distance from start to destination (in km)?
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A90 km
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B180 km
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C270 km
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D360 km
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ENone of these
Answer
Correct Answer: 180 km
Explanation
Introduction / Context:When two travellers cover the same distance at different speeds, the faster one arrives earlier. The difference in their times equals the given time gap, which leads to a simple equation in the unknown distance D that we can solve directly.
Given Data / Assumptions:
- Speeds: 30 km/h (A), 45 km/h (B).
- Arrival time difference = 2 h (B earlier).
- Same route and distance.
Concept / Approach:Times: t_A = D/30, t_B = D/45. Difference t_A − t_B = 2. Solve for D using common denominators.
Step-by-Step Solution:
D/30 − D/45 = 2.(1/30 − 1/45) = (3 − 2)/90 = 1/90.D * (1/90) = 2 ⇒ D = 180 km.Verification / Alternative check:Times: 180/30 = 6 h (A), 180/45 = 4 h (B); difference = 2 h as given.
Why Other Options Are Wrong:90 km gives 1 h gap; 270 km gives 3 h gap; 360 km gives 4 h gap—none match 2 h.
Common Pitfalls:Reversing which time is larger; forgetting to use the same distance in both fractions.
Final Answer:180 km