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3.(a)Three bells ring at regular interval of 9 min, 15 min and 21 min.The bells ring at 5.45 p.m.By 10.00 a.m next day,how many times will they have rung together? 3/9/16/21 (3marks

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Answer:

3 times (not including the first time at 5:45pm)

Step-by-step explanation:

Step 1

We need to first find out the time intervals at which all three bells will ring together after 5:45pm

The bells ring at intervals of 9, 15 and 21 minutes

To find the intervals at which all three bells ring together, find the Least Common Multiple (LCM) of 9, 15 and 21

LCM of 9, 15 and 21 can be found using prime factorization

  • Prime factors of 9:    3 × 3
  • Prime factors of 15:   3 x 5
  • Prime factors of 21:   3 x 7

LCM(9, 15, 21) = 3 x 3 x 5 x 7 = 315

So the bells will ring together every 315 minutes (5 hours and 15 minutes)

Step 2
Find the time difference between 5:45PM and 10:00 AM the next day and convert to minutes

  • Add 12 to 10:00 and then subtract 5:45 noting that 1 hour = 60 mins
    22:00 - 5:45 = 16 hours 15 minutes
  • Convert this time duration to minutes:
    16 hours 15 minutes = 16 × 60 + 15 = 975 minutes

Step 3
Find the number of integer 315 minute intervals in a time duration of 975 minutes

  • 975/315 = 3.095
  • Take the whole part: 3

Final Answer:
The bells will have rung a total of 3 times between 5:45pm(not included) and 10:00am the next day

Here are times at which the bells ring:
11:00 pm    
04:15 am  next day
09:30 am  next day

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