SOLUTION: Phyllis can rake our lawn in 50 minutes and I can do it in 40 minutes. If she rakes for five minutes before I join her, how long will take for us to finish?

Question 945014: Phyllis can rake our lawn in 50 minutes and I can do it in 40 minutes. If she rakes for five minutes before I join her, how long will take for us to finish?
Found 2 solutions by stanbon, macston:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Phyllis can rake our lawn in 50 minutes and I can do it in 40 minutes. If she rakes for five minutes before I join her, how long will take for us to finish?
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General idea: rate*time = work done
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Phyllis's rate:: 1/50 job/min
My rate:: 1/40 job/min
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Equation:
work + work = work done
(1/50)*5 + (1/40)x = 1
40*5 + 50x = 40*50
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200 + 50x = 2000
50x = 1850
x = 37 minutes (time for me to finish the job)
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Cheers,
Stan H.
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Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
Phyllis rakes 1 lawn in 50 min=1 lawn/50 min=1/50 lawn/min
I rake 1 lawn in 40 min=1 lawn/40 min=1/40 lawn/min
In the first five minutes, Phyllis rakes 5min(1/50 lawn/min)=5/50 lawn=1/10 lawn
Together Phyllis and I rake at a rate of 1/50 lawn/min + 1/40 lawn/min=
(Find common denominator) 4/4(1/50)lawn/min + 5/5(1/40) lawn/min=
4/200 lawn/min + 5/200 lawn/min= 9/200 lawn/min together
Phyllis has raked 1/10 of the lawn leaving 9/10 to rake (convert to 200ths)
20/20(9/10)lawn=180/200 lawn left to rake
together we rake 9/200 lawn/min so (180/200)/(9/200) min=20 minutes
ANSWER: It takes 20 additional minutes for both to finish the lawn.

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