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Machine A, working alone at its constant rate, produces x
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25 May 2016, 15:54
25 May 2016, 15:54
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Question Stats:
89% (01:45) correct
10% (01:36) wrong based on 167 sessions
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Machine A, working alone at its constant rate, produces x pounds of peanut butter in 12 minutes. Machine B, working alone at its constant rate, produces x pounds of peanut butter in 18 minutes. How many minutes will it take machines A and B, working simultaneously at their respective constant rates, to produce x pounds of peanut butter?
Show: :: Answer
7.2
Re: Machine A, working alone at its constant rate, produces x
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25 Dec 2018, 22:57
25 Dec 2018, 22:57
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Expert Reply
Try this, simple as possible
use the work formula:
Work= rate * time
W=rt
Machine A
Work= X
Rate is r
Time = 12
so ...
X=r*12
then the rate for machine a is X/12
Machine B
X=r*18
then the rate for machine b is X/18
add the two rates together
X/12 + X/18 = (6X+4X)/72 = 10X/72
remember that W=rt, but we have a rate now so then...
r=W/t
X is the unit of work, multiplied by 10/72, but remember, 10/72 is the reciprocal of time. which is 72/10==7.2
use the work formula:
Work= rate * time
W=rt
Machine A
Work= X
Rate is r
Time = 12
so ...
X=r*12
then the rate for machine a is X/12
Machine B
X=r*18
then the rate for machine b is X/18
add the two rates together
X/12 + X/18 = (6X+4X)/72 = 10X/72
remember that W=rt, but we have a rate now so then...
r=W/t
X is the unit of work, multiplied by 10/72, but remember, 10/72 is the reciprocal of time. which is 72/10==7.2
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Re: Machine A, working alone at its constant rate, produces x
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01 Jun 2016, 15:34
01 Jun 2016, 15:34
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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 job
Example: 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 job
Example: 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
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 job
Example: 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 job
Example: 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
