High School

Four bells begin to toll together at intervals of 6, 7, 8, and 9 seconds. What is the number of times they will toll together in 2 hours?

A. 11
B. 13
C. 14
D. 15

Answer :

The bells will toll together 15 times in 2 hours because their least common multiple occurs every 504 seconds, fitting into the 7200-second timeframe 14 times with a remainder, allowing for one additional tolling event.therefore the corect option D

First, we calculate the time in seconds for 2 hours:

[tex]\[ 2 \text{ hours} \times 60 \text{ minutes/hour} \tim[/tex] es 60[tex]\text{ seconds/minute} = 7200 \text{ seconds} \][/tex]

Next, we find the least common multiple (LCM) of the time intervals at which the bells toll:

[tex]\[ LCM(6, 7, 8, 9) = 2^3 \times 3^2 \times 7 = 504 \text{ seconds} \][/tex]

To determine how many times the bells will toll together in 2 hours, we divide the total time by the LCM:

[tex]\[ \frac{7200 \text{ seconds}}{504 \text{ seconds}} \approx 14 \text{ with a remainder of } 288 \text{ seconds} \][/tex]

The remainder of 288 seconds is less than the LCM, which means there will be one more instance of all the bells tolling together before the 2 hours are completed.

Therefore, the total number of times the bells will toll together in 2 hours is 14 + 1 = 15 times, which corresponds to option D.

therefore the corect option D

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