A and B start together and run in the same direction on a 3 km circular track. Their speeds are 200 m/min and 150 m/min respectively. After how long will they both be together again at the starting point?

Introduction / Context:To be together again at the start, each runner must have completed an integer number of laps. Thus, the rendezvous time at the start equals the least common multiple (LCM) of their individual lap times.

Given Data / Assumptions:

• Track length = 3,000 m.
• Speeds: 200 m/min and 150 m/min.

Concept / Approach:Lap times: T1 = 3,000/200 = 15 min; T2 = 3,000/150 = 20 min. Meeting at the start occurs at LCM(15, 20) min.

Step-by-Step Solution:

Verification / Alternative check:After 60 min, runner A has done 4 laps; runner B has done 3 laps—both at the start again.

Why Other Options Are Wrong:Other times are not common multiples of both 15 and 20 minutes.

Common Pitfalls:Using relative speed to compute the time they meet anywhere on track; here the location “starting point” forces an LCM approach.

Final Answer:1 hour