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Math Help - Can a 'how many minutes' question be solved using algebra?

  1. #1
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    Can a 'how many minutes' question be solved using algebra?

    I am reading a book of sample IQ test questions. One example of which, is the typical 'how many minutes' question.

    I can answer the question the long way, but I would be very interested to know if such questions can be solved more elegantly using algebra. I also hope this might provide a chance for brushing up my maths skills!

    Allow me to provide an example:

    Example question:
    'How many minutes is it before 12 noon, if 48 minutes ago it was twice as many minutes past 9am?'

    Answer:
    44 minutes'.
    - 12 noon less 44 minutes = 11:16am
    - 11:16am less 48 minutes = 10:28am
    - 0900am plus 88 minutes (44 x 2) = 10:28 am

    My question: Could this question be solved using a neat algebraic method?

    What do you think? Any advice would be much appreciated! Thank you
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  2. #2
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    Quote Originally Posted by Pipps View Post
    Example question:
    'How many minutes is it before 12 noon, if 48 minutes ago it was twice as many minutes past 9am?'

    Answer:
    44 minutes'.
    - 12 noon less 44 minutes = 11:16am
    - 11:16am less 48 minutes = 10:28am
    - 0900am plus 88 minutes (44 x 2) = 10:28 am
    M = number of minutes
    T = Time now

    So T+M = 12 noon.
    T - 48 = 9am + 2M.

    Let an hour be 60 minutes, so 12 noon = 720, and 9am = 540.
    (Changing from one day to the next could be a pain, but let's ignore that... )

    So you have T+M = 720
    and T - 48 = 540 + 2M.

    Two simultaneous equations for you to solve...

    Is that something like what you were looking for?
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  3. #3
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    Quote Originally Posted by Pipps View Post
    I am reading a book of sample IQ test questions. One example of which, is the typical 'how many minutes' question.

    I can answer the question the long way, but I would be very interested to know if such questions can be solved more elegantly using algebra. I also hope this might provide a chance for brushing up my maths skills!

    Allow me to provide an example:

    Example question:
    'How many minutes is it before 12 noon, if 48 minutes ago it was twice as many minutes past 9am?'

    Answer:
    44 minutes'.
    - 12 noon less 44 minutes = 11:16am
    - 11:16am less 48 minutes = 10:28am
    - 0900am plus 88 minutes (44 x 2) = 10:28 am

    My question: Could this question be solved using a neat algebraic method?

    What do you think? Any advice would be much appreciated! Thank you
    Let x denote the time in question, measured in minutes.

    Then you have

    12\ h-48\ min-x=9\ h+2x

    3\ h-48 \min = 3x Convert the hours into minutes:

    180\ min - 48\ min = 3x

    132\ min = 3x

    \boxed{44\ min = x}
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  4. #4
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    Unenlightened, I was quite sure how to make your suggested formula work.

    But Dear Earboth, your suggested formula worked perfectly for me! And it has worked in numerous similar situations since!

    But only once I worked out how you got from '12h -x = 9h +2x' to '3h = 3x'.

    I got there after a moment's thought, though. It was just that maths skills were a little rusty!
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