SOLUTION: You and a friend have decided to go into the lawn mowing business. Having done a particular yard several times you note the following. Working together you and your friend can mo

Question 148318: You and a friend have decided to go into the lawn mowing business. Having done a particular yard several times you note the following. Working together you and your friend can mow the yard in 3 hours. Working alone, it takes you 2 hours more than your friend to mow the yard. How long does it take your friend to mow the yard?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You and a friend have decided to go into the lawn mowing business. Having done a particular yard several times you note the following. Working together you and your friend can mow the yard in 3 hours. Working alone, it takes you 2 hours more than your friend to mow the yard. How long does it take your friend to mow the yard?
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Together:
Time = 3 hrs/job : Rate = 1/3 job//hr
----------
Friend:
Time = x hrs/job ; Rate = 1/x job/hr
----------
You:
Time = x+2 hrs/job ; Rate = 1/(x+2) job/hr
--------------
EQUATION:
rate + rate = together rate
1/x + 1/(x+2) = 1/3
Multiply thru by 3x(x+2)
3x+6 + 3x = x^2+2x
x^2-x-6 = 0
(x-3)(x+2) = 0
Positive answer:
x = 3 hrs (Your friend's time to do the job)
x+2 = 5 hrs ( Your time to do the job)
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Cheers,
Stan H.
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