Algebra

Bill can mow his mother's lawn in 45 minutes. His brother Jim can mow it in 75 minutes. How long will it take them to do it together?

Can someone help with with the work? But also an explanation of how it works? I want to understand this so I don't miss it on the test.

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asked by Eliza
  1. Bill's rate = 1lawn/45
    Jim's rate = 1lawn/75

    combined rate = 1lawn/45 + 1lawn/75
    = 8lawn/228

    time at combined rate = 1lawn/(8lawn/225)
    = 1lawn (225/8lawn)
    = 225/8
    = 28.125 minutes

    notice the "lawn" divided out, so we could really have used anything at all.
    Some students simply use 1 as the unit of whatever the task is.
    so combined rate = 1/45 + 1/75 = 8/225
    time at combined rate = 1/(8/225)
    = 225/8 = 28.125

    if you had 3 rates involved, you would get a combined rate by simply adding up the 3 rates, etc

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    posted by Reiny

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