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Question 161582This question is from textbook beginning and intermediate algebra
: it takes a teacher 45 minutes to grade a set of quizzes and takes her aide twice as long to do the same amount of grading. HOw long will it take them to grade a set of quizes if they work together? I try to work it out but i coul not. Please help me. thank you so much.
This question is from textbook beginning and intermediate algebra
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! it takes a teacher 45 minutes to grade a set of quizzes and takes her aide twice as long to do the same amount of grading. HOw long will it take them to grade a set of quizes if they work together? I try to work it out but i coul not. Please help me. thank you so much.
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It takes the teacher 45 mins and the aide 90 minutes to do the job.
It's obvious that working together it will take less than 45 minutes. Also, if they could both do the job in 45 mins, it makes sense that it would take half as long working together, or 22.5 minutes. Since the aide takes more than 45 mins, the answer should be more than 22.5 minutes, and less than 45 minutes. See that? That can serve as a check for the answer you come up with.
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The "trick" with this type of problem is to use "jobs/minute" rather than minutes per job. It's called the "reciprocal of the sum of the reciprocals", and it comes up in physical problems, like electricity.
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Call the pieces of the job "joblets."
For the teacher: 1/45 joblet per minute.
For the aide: 1/90 joblet per minute.
Together: 1/45 + 1/90
= 3/90 = 1/30 joblets/minute.
The inverse is 30 minutes per job together.
It is between 22.5 and 45, so it is acceptable.
It takes them 30 mins working together.
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