Question 115130: BEN AND REBECAA HACE TO MOW THE LAWN. WORKING ALONE, IT WOULD TAKE REBECAA TWO HOUR TO MOW THE LAWN. IT WOULD TAKE BEN 3HOURS. HOW LONG WOULD IT TAKE THEM WOKING TOGTHER.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Since Rebeca can mow the lawn by herself in two hours, her mowing rate is 1/2 of the lawn
per hour.
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Since Ben can mow the lawn by himself in three hours, each hour Ben mows 1/3 of the lawn.
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If they work together Rebeca mows (1/2)*T and Ben mows (1/3)*T where T is the time that it
takes them to complete the 1 job of mowing the lawn. In equation form this is:
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(1/2)*T + (1/3)*T = 1
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Recognize that (1/2) is equal to (3/6) and (1/3) is equal to (2/6). Substitute these into
the equation and you get:
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(3/6)*T + (2/6)*T = 1
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Since the terms on the left side now have the common denominator of 6, you can add them
by adding their numerators and placing that sum over the common denominator. This makes the
left side of the equation become:
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(3/6)*T + (2/6)*T = ((3+2)/6 )*T = (5/6)*T
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Substitute this for the left side of the equation and you have:
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(5/6)*T = 1
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You can now get rid of the denominator by multiplying both sides of this equation by
6. When you do, on the left side the multiplier 6 cancels with the 6 in the denominator. On
the right side you have 6 times 1. So the equation becomes:
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5*T = 6
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Solve for T by dividing both sides by 5 ... the multiplier of T and you get:
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T = 6/5 = 1.2
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So working together Rebeca and Ben can mow the lawn in 1.2 hours which is 1.2 times 60
minutes and that equals 72 minutes ... or 1 hour and 12 minutes.
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Hope this helps you to work the problem and understand how to do it.
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