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Chapter 2: Problem 46

A bell rings every 2 hours. A second bell rings every 3 hours. A third bell rings every 4 hours. If all three bells ring at 9:00 am, when will all three bells ring again? A. 12:00 pm B. \(2: 00 \mathrm{pm}\) C. 6:00 pm D. 9:00 pm

Short Answer

Expert verified
The next time all three bells will ring together is at \(9:00 \text{ pm}\). The answer is D. \(9:00 \text{ pm}\).

Step by step solution

01

List the multiples of each ringing time and find the common multiple

First, we need to list the multiples of the ringing interval for each bell: - Bell 1 (every 2 hours): 2, 4, 6, 8, 10, 12, 14, ... - Bell 2 (every 3 hours): 3, 6, 9, 12, 15, 18, ... - Bell 3 (every 4 hours): 4, 8, 12, 16, 20, 24, ... Then, we can observe that the least common multiple (LCM) of all the ringing intervals is 12, as that is the smallest multiple present in the multiples of all three bells.
02

Find out when they will ring together again

Since the LCM of the ringing intervals is 12, it means that all three bells will ring together every 12 hours. Since we know that all three bells last ringed together at 9:00 am, we simply need to add 12 hours to this time to find when they will ring together again. 9:00 am + 12 hours = 9:00 pm Hence, the next time all three bells will ring together is at 9:00 pm. The answer is D. 9:00 pm.

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