A church rings its bells every 15 minutes, the school rings its bells every 20 minutes and the day care center rings its bells every 25 minutes. If they all ring their bells at noon on the same day, at what time will they next all ring their bells together

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Mathematics

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1 May, 20:27

A church rings its bells every 15 minutes, the school rings its bells every 20 minutes and the day care center rings its bells every 25 minutes. If they all ring their bells at noon on the same day, at what time will they next all ring their bells together

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Carlo Ali · Answer 1

As few as just over 345 minutes (23*15) or as many as just under 375 minutes (25*15).

Imagine a simpler problem: the bell has rung just two times since Ms. Johnson went into her office. How long has Ms. Johnson been in her office? It could be almost as short as just 15 minutes (1*15), if Ms. Johnson went into her office just before the bell rang the first time, and the bell has just rung again for the second time.

Or it could be almost as long as 45 minutes (3*15), if Ms. Johnson went into her office just after the bells rang, and then 15 minutes later the bells rang for the first time, and then 15 minutes after that the bells rang for the second time, and now it's been 15 minutes after that.

So if the bells have run two times since Ms. Johnson went into her office, she could have been there between 15 minutes and 45 minutes. The same logic applies to the case where the bells have rung 24 times-it could have been any duration between 345 and 375 minutes since the moment we started paying attention to the bells!