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Thread: Jack & John

  1. #1
    Super Member harpazo's Avatar
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    Jack & John

    Jack can paint a wall in 3 hours. John can do the same job in 5 hours. How long will it take if they work together?

    Let x = time for both to get the job done

    (1/3) + (1/5) = 1/x

    15x[(1/3) + (1/5)] = 15x(1/x)

    5x + 3x = 15

    8x = 15

    x = 15/8

    Yes?
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  2. #2
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    Re: Jack & John

    Quote Originally Posted by harpazo View Post
    Jack can paint a wall in 3 hours. John can do the same job in 5 hours. How long will it take if they work together?

    Let x = time for both to get the job done

    (1/3) + (1/5) = 1/x

    15x[(1/3) + (1/5)] = 15x(1/x)

    5x + 3x = 15

    8x = 15

    x = 15/8

    Yes?
    Yes!!
    Some comments:
    1. An easier method to solve:
    $\displaystyle \frac{1}{3}+\frac{1}{5}=\frac{1}{x}$
    $\displaystyle \frac{8}{15} =\frac{1}{x}$
    $\displaystyle x=\frac{15}{8}$

    (Your method is correct but probably not the most efficient)

    2. $\displaystyle \frac{15}{8}$ hours = 1.875 hours = 1 hour 52.5 minutes or 1 hour 52 min 30 sec.

    (I always like to express answers to word problems using the language we would normally use. We would never say "it took 15/8 hours" but we would say "it took I hour 52 and a half minutes".)
    Thanks from harpazo
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  3. #3
    Super Member harpazo's Avatar
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    Re: Jack & John

    Quote Originally Posted by Debsta View Post
    Yes!!
    Some comments:
    1. An easier method to solve:
    $\displaystyle \frac{1}{3}+\frac{1}{5}=\frac{1}{x}$
    $\displaystyle \frac{8}{15} =\frac{1}{x}$
    $\displaystyle x=\frac{15}{8}$

    (Your method is correct but probably not the most efficient)

    2. $\displaystyle \frac{15}{8}$ hours = 1.875 hours = 1 hour 52.5 minutes or 1 hour 52 min 30 sec.

    (I always like to express answers to word problems using the language we would normally use. We would never say "it took 15/8 hours" but we would say "it took I hour 52 and a half minutes".)
    Good. Another one for my files.
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