Final answer:
To find the next time that all the bells will ring together, we need to find the least common multiple (LCM) of the ringing intervals of the bells. The first bell rings every 6 minutes, the second bell rings every 7 minutes, and the third bell rings every hour (or 60 minutes). The next time they will all ring together is at 12:42 PM.
Step-by-step explanation:
To find the next time that all the bells will ring together, we need to find the least common multiple (LCM) of the ringing intervals of the bells.
The first bell rings every 6 minutes, the second bell rings every 7 minutes, and the third bell rings every hour (or 60 minutes).
To find the LCM, we can list out the multiples of each interval and find the smallest common multiple:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60...
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70...
Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600...
We can see that the first time all three bells will ring together is at the 42nd minute. Therefore, they will next all ring together at 12:42 PM.