# 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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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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