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Question 132055: Using a new lawn mower, Abby can mow the lawn in 2 hours. Her sister Carla uses an older mower and takes 3 huors to mow the same lawn. How long will it take them if they work together? Please tell me how you answer it. That would be awesome.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Since Abby can mow the lawn in 2 hours, that means that each hour she does 1/2 of the lawn.
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Since Carla mows the lawn in 3 hours, each hour she mows she does 1/3 of the lawn.
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If they work together for T hours then for completing the 1 job it will take them:
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(1/2)*T + (1/3)*T = 1
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You can factor the T and the equation becomes:
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T*(1/2 + 1/3) = 1
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1/2 equals 3/6 and 1/3 = 2/6. Substituting these equivalent values into the equation results
in:
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T*(3/6 + 2/6) = 1
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Since the two fractions now have the same denominator, they can be combined by adding their
numerators over the common denominator ... and this makes the equation become:
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T*5/6 = 1
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Get rid of the denominator 6 by multiplying both sides of the equation by 6 to convert the
equation to:
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T*5 = 6
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Solve for T by dividing both sides of the equation by 5 and you have:
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T = 6/5 = 1.2
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and 1.2 hours is the same as 60 minutes times 1.2 which is 72 minutes. And 72 minutes is
1 hour and 12 minutes.
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So working together the two ladies can mow the complete lawn in 1 hour and 12 minutes.
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Hope this helps you to understand the problem a little better.
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