SOLUTION: Working alone, Jess can rake leaves off a lawn in 50 minutes. Working alone, cousin Tate can do the same job in 30 minutes. Today they are going to work together, Jess starting t o

Question 845344: Working alone, Jess can rake leaves off a lawn in 50 minutes. Working alone, cousin Tate can do the same job in 30 minutes. Today they are going to work together, Jess starting t one end of the lawn and Tate starting simultaneously at the other end. In how many minutes will they meet and thus have the lawn completely raked?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Working alone, Jess can rake leaves off a lawn in 50 minutes.
Jess rate = 1/50 job/min
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Working alone, cousin Tate can do the same job in 30 minutes.
Tate rate = 1/30 job/min
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Today they are going to work together, Jess starting at one end of the lawn and Tate starting simultaneously at the other end. In how many minutes will they meet and thus have the lawn completely raked?
Together rate = 1/x job/min
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Equation:
rate + rate = together rate
1/50 + 1/30 = 1/x
-----
30x + 50x = 30*50
80x = 30*50
x = (3/8)50
----
x = 18.75 = 18 min 40 sec (time to do the job together)
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Cheers,
Stan H.
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