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Math Help - Mean time and varying inversely

  1. #1
    Senior Member Mukilab's Avatar
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    Mean time and varying inversely

    Amy had 30 CDs

    The mean playing time of these was 42mins

    She sold 5
    The mean playing time of the 25 left is now 42.8
    Calculate the mean playing time of the 5 CDs that Amy sold.

    Method please.


    2)She shutter speed S of a camera varies inversely as the square of the aperture setting, F. When F=8, S=125. Is this the same as the proportional formula where F=KS?
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  2. #2
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    Quote Originally Posted by Mukilab View Post
    Amy had 30 CDs

    The mean playing time of these was 42mins

    She sold 5
    The mean playing time of the 25 left is now 42.8
    Calculate the mean playing time of the 5 CDs that Amy sold.

    Method please.


    2)She shutter speed S of a camera varies inversely as the square of the aperture setting, F. When F=8, S=125. Is this the same as the proportional formula where F=KS?
    1) Let a = \frac{t_1 + t_2 + .... + t_{25}}{30} and b = \frac{t_{26} + .... + t_{30}}{30} . Then:

    42 = \frac{a + b}{30} .... (1)

    42.8 = \frac{a}{25} .... (2)

    Solve equations (1) and (2) simultaneously to calculate the value of \frac{b}{30}.


    2) No. S = \frac{k}{F^2}.
    Last edited by mr fantastic; January 8th 2010 at 01:21 PM.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    1) Let a = \frac{t_1 + t_2 + .... + t_{25}}{30} and b = \frac{t_{26} + .... + t_{30}}{30} . Then:

    42 = \frac{a + b}{30} .... (1)

    42.8 = \frac{a}{25} .... (2)
    Since you defined a with a denominator of 30, shouldn't this be
    42.8= \frac{a}{25}(30)? Otherwise you are going to get a negative number for b.

    Solve equations (1) and (2) simultaneously to calculate the value of \frac{b}{30}.


    2) No. S = \frac{k}{F^2}.
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  4. #4
    Senior Member Mukilab's Avatar
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    Quote Originally Posted by HallsofIvy View Post
    Since you defined a with a denominator of 30, shouldn't this be
    42.8= \frac{a}{25}(30)? Otherwise you are going to get a negative number for b.

    I found that and assumed it was right :/
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  5. #5
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    Quote Originally Posted by HallsofIvy View Post
    Since you defined a with a denominator of 30, shouldn't this be
    42.8= \frac{a}{25}(30)? Otherwise you are going to get a negative number for b.
    Thankyou. Yes, a slip-up on my part.
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