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)?

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:

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