30 minutes to Correct 150 Quizzes - Algebra 1 Problem

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    Algebra Algebra 1
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SUMMARY

The problem involves calculating the time it takes for Mr. Jacobs and his student aide to correct 150 quizzes together. Mr. Jacobs can correct 150 quizzes in 50 minutes, while his aide takes 75 minutes for the same task. By determining their individual rates—3 quizzes per minute for Mr. Jacobs and 2 quizzes per minute for the aide—they can collectively correct 5 quizzes per minute. Therefore, it will take them 30 minutes to correct 150 quizzes together.

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AznBoi
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I'm confused on how to solve this problem effectively. I have solved it using my own "weird" way. I will post my solution but please post others that may be more understandable. Thanks.

Problem: Mr. Jacobs can correct 150 quizzes in 50 minutes. His student aide can correct 150 quizzes in 75 minutes. Working together, how many minutes will it take them to correct 150 quizzes?

My solution:
150q/50m = 15/5=3x

150q/75m= 2x

2x+3x=5x=150

x=30 ..lol
 
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Think of correcting 150 quizes as "one job". The problem description involves rates. Rate * Time = Jobs

Mr. Jacobs: 1 job per 50 minutes
student aid: 1 job per 75 minutes

Similar to rate*time=distance, these rates may be additive if Mr. Jacobs and his aid work together.
 
Actually, your "weird" way is perfectly reasonable- you calculated the rate at which they correct grades: Mr. Jacobs corrects 3 quizzes per minute and his aid corrects 2 quizzes per minute. Together they correct 5 quizzes per minute.
 

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