SOLUTION: Two teachers are grading math homework. One teacher can grade a stack of papers in 50 minutes and the other can complete the job in 100 minutes. How long does it take them to grade
Question 156139: Two teachers are grading math homework. One teacher can grade a stack of papers in 50 minutes and the other can complete the job in 100 minutes. How long does it take them to grade all the papers if the first teacher grades alone for 23 minutes, then they work together to finish? Found 2 solutions by stanbon, Earlsdon:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Two teachers are grading math homework.
One teacher can grade a stack of papers in 50 minutes: rate = 1/50 papers/minute
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the other can complete the job in 100 minutes: rate = 1/100 papers/minute
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Together rate = 1/50 + 1/100 = 3/100 papers/min
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How long doesit take them to grade all the papers if the first teacher grades alone for 23 minutes, then they work together to finish?
EQUATION:
rate*time = work done
(1/50)23 + x(3/100) = 1 job done
(46/100) + 3x/100 = 1
46 + 3x = 100
3x = 54
x = 18 minutes (time it will take to finish the job)
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Cheers,
Stan H.
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You can put this solution on YOUR website! Nice job Stanbon! ...but don't forget to add the 23 minutes taken by the first teacher to the 18 minutes taken by both of them, so it takes a total of 41 minutes to finish the job.
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