Question

A college offers shuttle service from Olney Hall or Lot B to its campus quad. Both shuttles first depart their locations at ​9:15 A.M. They run from each location to campus and back at the intervals shown. When is the next time both shuttles will depart for Campus at the same​ time?

Answer 1

The next time both shuttles will depart for campus at the same time can be determined by finding the least common multiple (LCM) of the intervals at which each shuttle departs.

Let's list the intervals for each shuttle:

- Shuttle from Olney Hall departs every 30 minutes.

- Shuttle from Lot B departs every 45 minutes.

To find the LCM, we can list the multiples of each interval until we find a common multiple:

Multiples of 30 minutes: 30, 60, 90, 120, 150, 180, ...

Multiples of 45 minutes: 45, 90, 135, 180, ...

We can see that the least common multiple of 30 and 45 is 90 minutes.

Therefore, the next time both shuttles will depart for campus at the same time is 90 minutes after their initial departure at 9:15 A.M. This would be at 10:45 A.M.