using a new lawn mower,abby can mow the lawn in 2 hours.her sister carla uses an old mower and take 3 hours to mow the same lawn how long will it take them if tey work together?
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Answers
Answer:
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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.