Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job?
A. 4/5
B. 9/4
C. 11/4
D. 4
E. 13/2
OA: B
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Work rate problem
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Jay@ManhattanReview
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Hi Mo2men,Mo2men wrote:Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job?
A. 4/5
B. 9/4
C. 11/4
D. 4
E. 13/2
OA: B
This is a typical Work and Rate problem.
We have rates of machines A, B and C: 10 hr, 4 hr, and 5 hr to complete a job.
The part of talk A can complete in 1 hour = 1/10;
The part of talk B can complete in 1 hour = 1/4;
The part of talk C can complete in 1 hour = 1/5;
Thus, together in 1 hour A, B and C together can complete 1/10 + 1/4 + 1/5 = 11/20 part of work
Thus, the part of work to be done bt C alone = 1 - 11/20 = 9/20
Since C completes 1/5 part of task in 1 hour, it would take (9/20) / (1/5) = (9/20)*5 = 9/4 hours.
The correct answer: B
Hope this helps!
Relevant book: Manhattan Review GMAT Word Problems Guide
-Jay
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Let the job = the LCM of 10, 4 and 5 = 20 widgets.Mo2men wrote:Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job?
A. 4/5
B. 9/4
C. 11/4
D. 4
E. 13/2
Since A takes 10 hours to produce 20 widgets, A's rate = w/t = 20/10 = 2 widgets per hour.
Since B takes 4 hours to produce 20 widgets, B's rate = w/t = 20/4 = 5 widgets per hour.
Since C takes 5 hours to produce 20 widgets, C's rate = w/t = 20/5 = 4 widgets per hour.
Combined rate for A+B+C = 2+5+4 = 11 widgets per hour.
After A, B and C work together for an hour to produce 11 widgets, the remaining work = 20-11 = 9 widgets.
Since C's rate = 4 widgets per hour, the time for C to produce the remaining 9 widgets = w/r = 9/4 hours.
The correct answer is B.
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these problems can be solved using this equation.
Job/hour * hours = job
a does .1 jobs per hour. B does .25, and c does .2
together in one hour they do .55 of the job. So .45 of the job is left
.45 is = to .05 (9) or (1/20)(9)
Since C takes 5 hours to complete the job he takes 5/20 or 1/4 of an hour to complete 1/20 the job. To complete 9/20 the job he needs to take 9/4 hours.
or we can set up a ratio. 1 job/5 hours = (9/20) jobs / x hours
5*(9/20)= 45/20=(9/4) hours
You can also be sort of "cheap" and reason that since, he takes 5 hours to do the job, doing half the job will take him 2.5 hours. He has slightly less than half the job to do and only 9/4 hours matches that.
The key to work problems imo is to understand the equation
job/hour * hours = job
The second key is to understand that you can add job/hour for multiple people.
If one person does 1/5 of the job per hour and another does 1/4 of the job per hour, then together they do the sum of that together per hour. Making a table can help especially if you are first getting started on these types of problems.
Job/hour * hours = job
a does .1 jobs per hour. B does .25, and c does .2
together in one hour they do .55 of the job. So .45 of the job is left
.45 is = to .05 (9) or (1/20)(9)
Since C takes 5 hours to complete the job he takes 5/20 or 1/4 of an hour to complete 1/20 the job. To complete 9/20 the job he needs to take 9/4 hours.
or we can set up a ratio. 1 job/5 hours = (9/20) jobs / x hours
5*(9/20)= 45/20=(9/4) hours
You can also be sort of "cheap" and reason that since, he takes 5 hours to do the job, doing half the job will take him 2.5 hours. He has slightly less than half the job to do and only 9/4 hours matches that.
The key to work problems imo is to understand the equation
job/hour * hours = job
The second key is to understand that you can add job/hour for multiple people.
If one person does 1/5 of the job per hour and another does 1/4 of the job per hour, then together they do the sum of that together per hour. Making a table can help especially if you are first getting started on these types of problems.
