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Math Help - Two Cuckoo Clocks

  1. #1
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    Two Cuckoo Clocks

    I have a maths problem and wanted to know if there was an easier way or a formula to work it out, rather than go through each time which is taking ages.

    Problem - "Two cuckoo clocks were brought to the Tick Tock Clock Shop for repairs. Both clocks always told the correct time. However, one cuckoo came out every 45 minutes and the other came out every 55 minutes. One day, both cuckoos came out at 12.00 noon. When was the next time both cuckoos came out together."

    If someone knows a way of working it out, that would be great. Thanks.
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  2. #2
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    List the times of both clocks until they match

    C_{45}: 12,12:45,1:30,2:15,\dots

    C_{55}: 12, 12:55,1:50,2:45,\dots
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  3. #3
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by stormtigershark View Post
    I have a maths problem and wanted to know if there was an easier way or a formula to work it out, rather than go through each time which is taking ages.

    Problem - "Two cuckoo clocks were brought to the Tick Tock Clock Shop for repairs. Both clocks always told the correct time. However, one cuckoo came out every 45 minutes and the other came out every 55 minutes. One day, both cuckoos came out at 12.00 noon. When was the next time both cuckoos came out together."

    If someone knows a way of working it out, that would be great. Thanks.
    Take LCM(45,55) = 495.

    Then see that 495 = 8*60 + 15, meaning 8 hrs 15 minutes.

    So, that makes 8:15 PM.
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  4. #4
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    Quote Originally Posted by pickslides View Post
    List the times of both clocks until they match

    C_{45}: 12,12:45,1:30,2:15,\dots

    C_{55}: 12, 12:55,1:50,2:45,\dots

    Thanks, but that's what I was originally doing. I wanted to know if there was a quicker way or a formula for this type of question.
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  5. #5
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    Quote Originally Posted by undefined View Post
    Take LCM(45,55) = 495.

    Then see that 495 = 8*60 + 15, meaning 8 hrs 15 minutes.

    So, that makes 8:15 PM.

    Thanks for the formula.
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  6. #6
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    Quote Originally Posted by stormtigershark View Post
    "Two cuckoo clocks were brought to the Tick Tock Clock Shop for repairs.
    Ad for Tick Tock Clock Shop: "If your clock don't tick, tock to us !"
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  7. #7
    Senior Member Mukilab's Avatar
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    Quote Originally Posted by stormtigershark View Post
    Thanks for the formula.
    Its not a formula, merely another method
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