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 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)   (Show Source): You can put this solution on YOUR website!

Answer by josgarithmetic(39621)   (Show Source): You can put this solution on YOUR website!
"one teacher", same as "first teacher", stack per minutes
Other teacher, 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.

Simplify and solve for x.

-

The two work together for 18 minutes.
Total time doing the grading was 23+18=41 minutes.
Answer by MathTherapy(10555)   (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: =======>
T + 2T + 46 = 100 ------ Multiplying by LCD, 100
3T = 54
Time taken by both to complete job, or
Time taken to grade ALL =
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