Question

The UMD Circulator is a free shuttle for University of Maryland students on campus. The circulator stops in front of the library every 12 minutes. A Metro bus also stops at the campus library every 15 minutes. At 6 AM both the shuttle and the bus arrive at the library. When is the next time the circulator and Metro bus will arrive at the library at the same time?

Answer 1

that depends on the time they start

Answer 2

The UMD Circulator and the Metro bus will next arrive at the campus library at the same time at 7 AM, which is determined by calculating the Least Common Multiple (60 minutes) of their arrival intervals, 12 and 15 minutes.

Step-by-step explanation:

The question asks when the UMD Circulator, a free shuttle for the University of Maryland students, and the Metro bus, which both stop at the campus library, will arrive at the same time again after their simultaneous arrival at 6 AM. To find the next time these two transportation services will coincide at the library stop, we need to calculate the Least Common Multiple (LCM) of their arrival intervals. The Circulator arrives every 12 minutes, and the Metro bus arrives every 15 minutes.

To find the LCM of 12 and 15, we list the multiples of each number until we find a common multiple.

• Multiples of 12: 12, 24, 36, 48, 60, ...
• Multiples of 15: 15, 30, 45, 60, ...

The smallest common multiple between 12 and 15 is 60 minutes. Therefore, after their initial meeting at 6 AM, the Circulator and Metro bus will both arrive at the library again 60 minutes later, which will be at 7 AM.