Question

A college offers shuttle service from Dickson Hall or Lot B to its
campus quad. Both shuttles first depart their locations at 9:10 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?
College Shuttle
Departs from:
Lot B
Every 10 minutes
Dickson Hall
Every 12 minutes
First shuttles leave at 9:10 A.M.
​

Answer 1

Answer:

At 10:30 A.M.

Step-by-step explanation:

A college offers shuttle service from Dickson Hall or Lot B to its  campus quad.

At 9:10 A.M the first shuttle leaves from their locations for the campus.

If the shuttles leave from Lot B every 10 minutes and leave from Dickson Hall every 12 minutes, then both the shuttles will leave their origin at the same time after 60 minutes.

This is because 60 is the smallest multiple of 10 and 12 which is common for them.

Therefore, 10:30 A.M. is the next time when both shuttles will depart for the campus at the same time. (Answer)

Answer 2

Answer:

10:10 am

Step-by-step explanation:

Multiples of 12: 12,24,36,48,60. Then the lowest common factor of 10 minutes and 12 minutes is 60 minutes.

If the first college shuttle  departs from Lot B at 9:10 A.M then the sixth will depart 6*10 = 60 minutes late, that is at 10:10 am

If the first college shuttle  departs from Dickson Hall at 9:10 A.M then the fifth will depart 5*12 = 60 minutes late, that is at 10:10 am