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Four bells begin to toll together and toll respectively at intervals of 6, 7, 8, and 9 seconds. In 1.54 hours, how many times do they toll together and at what interval (in seconds)?

A. 14, 504
B. 14, 480
C. 12, 504
D. 16, 580

Answer :

The bells toll together 12 times in 1.54 hours, at intervals of 504 seconds after finding the least common multiple of their tolling intervals. Therefore, option C. 12, 504 is the correct answer.

To determine how many times the bells toll together in 1.54 hours and at what interval, we will first convert the time into seconds and then find the least common multiple (LCM) of the tolling intervals of the bells.

1.54 hours is equal to 1.54 imes 3600 seconds, which is 5544 seconds.

The intervals at which the bells toll are 6, 7, 8, and 9 seconds. We need to find the LCM of these numbers:

  • LCM(6, 7, 8, 9) = 504 seconds.

This LCM means the bells toll together every 504 seconds.

To find the total number of times the bells toll together in 5544 seconds, we divide 5544 by 504:

5544 / 504 = 11 times.

However, the bells toll together for the first time at the start of the period, so we must add 1 to this number:

11 + 1 = 12 times.

Therefore, the bells toll together 12 times in 1.54 hours, at intervals of 504 seconds.

herefore, option C. 12, 504 is the correct answer.

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