Final answer:
To find the time at which a bus to Alton and a bus to Fleet leave at the same time, we need to find the least common multiple (LCM) of 6 minutes and 8 minutes. The LCM of 6 and 8 is 24 minutes, so the next departure time will be 10:24 am.
Step-by-step explanation:
To find the time at which a bus to Alton and a bus to Fleet leave at the same time, we need to find the least common multiple (LCM) of 6 minutes and 8 minutes. The LCM is the smallest multiple that both numbers have in common.
The multiples of 6 minutes are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,...
The multiples of 8 minutes are: 8, 16, 24, 32, 40, 48, 56, 64,...
The least common multiple of 6 and 8 is 24 minutes.
Therefore, a bus to Alton and a bus to Fleet will next leave at the same time 24 minutes after they both left at 10 am. The next departure time will be at 10:24 am.