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

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Question 1138502: 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 3 solutions by ikleyn, josgarithmetic, MathTherapy:
Answer by ikleyn(52817) About Me  (Show Source):
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
"one teacher", same as "first teacher", 1%2F50 stack per minutes
Other teacher, 1%2F100 stack per minutes

First teacher works for 23 minutes and then both teachers work together for x minutes, in order to grade 1 stack of papers.

%281%2F50%29%2A23%2B%281%2F50%2B1%2F100%29%2Ax=1
Simplify and solve for x.

-

23%2F50%2B%282%2F100%2B1%2F100%29x=1
46%2F100%2B3x%2F100=1
46%2B3x=100
3x=54
highlight%28x=18%29
The two work together for 18 minutes.
Total time doing the grading was 23+18=41 minutes.

Answer by MathTherapy(10555) About Me  (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 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?
Let time taken for both to grade the remaining papers be T

Then time (singly and in tandem) taken by the 1st = T + 23

We then get:  =======> matrix%281%2C3%2C+T%2F100+%2B+%28T+%2B+23%29%2F50%2C+%22=%22%2C+1%29

T + 2T + 46 = 100 ------ Multiplying by LCD, 100

3T = 54

Time taken by both to complete job, or matrix%281%2C6%2C+T%2C+%22=%22%2C+54%2F3%2C+%22=%22%2C+18%2C+minutes%29

Time taken to grade ALL = highlight_green%28matrix%281%2C4%2C+23+%2B+18%2C+%22=%22%2C+41%2C+minutes%29%29