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Math Help - I know the answer and the formula but I can not get the right answer ?

  1. #1
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    I know the answer and the formula but I can not get the right answer ?

    sally can paint a house in 4 hours and john can paint the same house in 6 hourse how long does it take for them to paint the same house together. I know the answer in 2 hours and 24 mins. and I know that we use D=RT but I can not get 2 hours and 24 mins from it. Please help. thank you.
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  2. #2
    Senior Member Peritus's Avatar
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    sally can paint a house in 4 hours - \frac{1}<br />
{4}\frac{{house}}<br />
{{hour}}

    john can paint the same house in 6 hourse - \frac{1}<br />
{6}\frac{{house}}<br />
{{hour}}


    together - \frac{1}<br />
{{\frac{1}<br />
{6} + \frac{1}<br />
{4}}} = \frac{{12}}<br />
{{3 + 2}} = 2\frac{2}<br />
{5} = 2\quad hours\quad and\quad 24\quad \min utes
    Last edited by Peritus; March 26th 2008 at 02:44 PM.
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  3. #3
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    Another way with same result

    4 hours = 4* 60 = 240 minutes
    6 hours = 6*60 = 360 minutes

    1/240 + 1/360 = 1/t

    (multiply both side by t): t/240 + t/360 = 1

    (get common denominator): 3t/720 + 2t/720 = 1

    5t/720 = 1

    (multiply both sides by 720) 5t = 720

    (divide both sides by 5) t = 720/5

    t = 144 minutes

    (convert to hours):
    t = 144/60 = 2 hours + (144 120 minutes) = 2 hours 24 minutes
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  4. #4
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    simplest way is : let x= time . Person one is 1 house/4 hours and two is 1/6. so 1/4*x+1/6*x=1. that is x(10/24)=1 then that is 12/5 hours =x. convert that is 2 hours and 24 min.
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