Machine A and machine B process the same work at different rates. Machine C processes work as fast as Machines A & B combined. Machine D processes work three times as fast as Machine C; Machine D's work rate is also exactly four times Machine B's rate. Assume all four machines work at fixed unchanging rates. If Machine A works alone on a job, it takes 5 hours and 40 minutes. If all four machines work together on the same job simultaneously, how long will it take all of them to complete it?
A. 8 minutes
B. 17 minutes
C. 35 minutes
D. 1 hour and 15 minutes
E. 1 hours and 35 minutes
The OA is B.
Please, can anyone explain this PS question? I tried to solve it but I can't get the correct answer. Thanks.
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Machine A and machine B process the same work at different
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Keith@ThePrincetonReview
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The information in the question stem can be used to write several equations, relating the rates at which the different machines work.swerve wrote:Machine A and machine B process the same work at different rates. Machine C processes work as fast as Machines A & B combined. Machine D processes work three times as fast as Machine C; Machine D's work rate is also exactly four times Machine B's rate. Assume all four machines work at fixed unchanging rates. If Machine A works alone on a job, it takes 5 hours and 40 minutes. If all four machines work together on the same job simultaneously, how long will it take all of them to complete it?
A. 8 minutes
B. 17 minutes
C. 35 minutes
D. 1 hour and 15 minutes
E. 1 hours and 35 minutes
The OA is B.
Please, can anyone explain this PS question? I tried to solve it but I can't get the correct answer. Thanks.
Machine C works as fast as Machines A and B combined, so C = A + B.
Machine D works three times as fast as Machine C, so D = 3C, and C = (1/3)D.
Machine D works four times as fast as Machine B, so D = 4B, and B = (1/4)D.
Substitute these expressions for B and C into the first equation above, so that (1/3)D = A + (1/4)D.
Rewrite this equation using a common denominator, so that (4/12)D = A + (3/12)D.
Simplify this equation, so that A = (1/12)D.
Machine A works at a rate of 1 job in 5 hours and 40 minutes, or 1 job in 340 minutes. Thus, Machine A works at a rate of 1/340.
Substituting this value into the equation yields the equation 1/340 = (1/12)D.
Simplify, so that D = 12/340, or 12 jobs in 340 minutes.
Then, if B = (1/4)D, it must be the case that B = 3/340. In other words, Machine B works at a rate of 3 jobs every 340 minutes.
And if C = (1/3)D, it must be the case that C = 4/340. In other words, Machine C works at a rate of 4 jobs every 340 minutes.
Add the rates of the 4 machines, so that A + B + C + D = (1/340) + (3/340) + (4/340) + (12/340) = 20/340.
Reduce the fraction, so that all 4 machines working together have a combined rate of 1/17, or 1 job every 17 minutes.
The correct answer is choice B.
Hope this helps.
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Machine D processes work three times as fast as Machine C.swerve wrote:Machine A and machine B process the same work at different rates. Machine C processes work as fast as Machines A & B combined. Machine D processes work three times as fast as Machine C; Machine D's work rate is also exactly four times Machine B's rate. Assume all four machines work at fixed unchanging rates. If Machine A works alone on a job, it takes 5 hours and 40 minutes. If all four machines work together on the same job simultaneously, how long will it take all of them to complete it?
A. 8 minutes
B. 17 minutes
C. 35 minutes
D. 1 hour and 15 minutes
E. 1 hours and 35 minutes
Machine D's work rate is also exactly four times Machine B's rate.
Let D = 12 units per minute, implying that C= 4 units per minute and B = 3 units per minute.
Machine C processes work as fast as Machines A and B combined.
Since C = 4 units per minute and B = 3 units per minute, A = 1 unit per minute.
If Machine A works alone on a job, it takes 5 hours and 40 minutes.
Since A working at 1 unit per minute takes 340 minutes to complete the job, we get:
Job = rt = (1)(340) = 340 units.
If all four machines work together on the same job simultaneously, how long will it take all of them to complete it?
Since the combined rate for A+B+C+D = 1+3+4+12 = 20 units per minute, the time for all 4 machines together to complete the 340-unit job = w/r = 340/20 = 17 minutes.
The correct answer is B.
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Scott@TargetTestPrep
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Since Machine A's time to complete the job is 5 hours and 40 minutes, or 5 2/3 = 17/3 hours, its rate is 3/17. We can let Machines B's rate = b and thus, Machine C's rate = 3/17 + b and Machine D's rate = 3(3/17 + b) = 9/17 + 3b. We are also given that Machine D's rate = 4b. Thus we have:swerve wrote:Machine A and machine B process the same work at different rates. Machine C processes work as fast as Machines A & B combined. Machine D processes work three times as fast as Machine C; Machine D's work rate is also exactly four times Machine B's rate. Assume all four machines work at fixed unchanging rates. If Machine A works alone on a job, it takes 5 hours and 40 minutes. If all four machines work together on the same job simultaneously, how long will it take all of them to complete it?
A. 8 minutes
B. 17 minutes
C. 35 minutes
D. 1 hour and 15 minutes
E. 1 hours and 35 minutes
9/17 + 3b = 4b
9/17 = b
Now, we can determine that C's rate = 3/17 + 9/17 = 12/17 and D's rate = 4(9/17) = 36/17.
Thus, if we let x = the time, in hours, for the 4 machines to work together to complete the job, we have:
(3/17)x + (9/17)x + (12/17)x + (36/17)x = 1
[(3 + 9 + 12 + 36)/17]x = 1
(60/17)x = 1
x = 1/(60/17) = 17/60
Thus it takes 17/60 hours, or 17 minutes to complete the job when 4 machines work together.
Answer: B
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