Explanation
For work questions, there are two useful rules:
Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the jobExample: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour
Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire jobExample: If Sam can complete 1/8 of the job
in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.
Let’s use these rules to solve the question. . . .
For this question, let's say that
the entire job consists of making x pounds of peanut butter. Machine A completes the entire job in 12 minutes.So, using
Rule #1, machine A completes 1/12 of the job in ONE MINUTE
Machine B completes the entire job in 18 minutes.So, using
Rule #1, machine B completes 1/18 of the job in ONE MINUTE
When we COMBINE their efforts, they can complete (1/12 + 1/18) of the job in ONE MINUTE
1/12 + 1/18 = 3/36 + 2/26 = 5/36
So, COMBINED the machines can complete 5/36 of the job in ONE MINUTE
When we apply
Rule #2, the amount of time to complete the ENTIRE JOB = 36/5 minutes
Answer: 36/5 minutes or 7.2 minutes
Cheers,
Brent
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Brent Hanneson - founder of Greenlight Test Prep