Two cars A and B travel from one city to another at constant speeds of 72 km/h and 90 km/h respectively. If car B takes 1 hour less than car A to cover the full journey, what is the distance between the two cities in kilometres?

Introduction / Context: This is another time and distance question involving two cars with different speeds covering the same distance. The difference in their travel times is known, and you must determine the distance using basic algebra. It reinforces the relationship between speed, distance and time. Given Data / Assumptions:

• Speed of car A = 72 km/h.
• Speed of car B = 90 km/h.
• Distance between the cities = D km (unknown).
• Car B takes 1 hour less than car A.
• Both cars travel at constant speed without stops.

Concept / Approach: For each car, time is distance divided by speed. Since both cover the same distance D, the difference in their times can be expressed in terms of D. We create one equation using the given 1 hour difference and then solve for D. Step-by-Step Solution: Let D be the distance in km. Time taken by A = D / 72 hours. Time taken by B = D / 90 hours. Given that car B is faster and takes 1 hour less than car A: D / 72 - D / 90 = 1. Compute 1/72 - 1/90 = (90 - 72) / (72 * 90) = 18 / 6480 = 1 / 360. So (1 / 360) * D = 1, hence D = 360 km. Verification / Alternative check: Time for A with D = 360 km: 360 / 72 = 5 hours. Time for B: 360 / 90 = 4 hours. Difference = 5 - 4 = 1 hour, which matches the condition. Why Other Options Are Wrong: 270 km gives times 270/72 and 270/90, difference less than 1 hour. 240 km produces times whose difference is 240 * (1/72 - 1/90) = 240 / 360 = 2/3 hour, not 1 hour. 400 km gives difference 400 / 360 = 1.11 hours approximately, which is larger than required. Common Pitfalls: Confusing which time is larger can lead to writing D / 90 - D / 72 = 1, which gives a negative distance. Some candidates directly try to plug in option distances without simplifying fractions, which is slower and more error prone. Always remember time = distance / speed, and derive a simple equation before calculating. Final Answer: The distance between the two cities is 360 km.