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10 Oct 2021, 05:30
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E
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Difficulty:
55%
(hard)
Question Stats:
71% (02:54) correct
29%
(03:14)
wrong
based on 176
sessions
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A factory has three machines, Machine A, Machine B and Machine C, each of which works at a constant rate. At the beginning of the day, Machine A worked alone for 3 hours and completed \(\frac{1}{6}\) of a certain job. Machine A then worked together with Machine B for 2 hours, during which time \(\frac{1}{3}\) of the job was completed. Finally, Machine B and Machine C worked together for 4 hours and completed the remainder of the job. How long would it have taken Machine C, working alone, to complete the job?
A) 9 hours
B) 12 hours
C) 18 hours
D) 36 hours
E) 72 hours
A) 9 hours
B) 12 hours
C) 18 hours
D) 36 hours
E) 72 hours
01 Nov 2021, 22:48
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Quote:
Using RT=W
Let rate of machine A, machine B, machine C be x, y and z respectively.
Machine A worked alone for 3 hours and completed 1/6 of a certain job
x*3 = 1/6
x = 1/18
Machine A then worked together with Machine B for 2 hours, during which time 1/3 of the job was completed
(x+y)*2 = 1/3
1/18 + y = 1/6
y = 1/6 - 1/18
y = 1/9
Machine B and Machine C worked together for 4 hours and completed the remainder of the job
Amount of the work remaining = 1 -(1/6 + 1/3) = 1/2
(y+z)*4 = 1/2
1/9 + z = 1/8
z = 1/8 - 1/9
z = 1/72
It would take 72 hours for Machine C to complete the job, working alone.
E is correct
08 Sep 2024, 18:58
Kudos
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A factory has three machines, Machine A, Machine B and Machine C, each of which works at a constant rate. At the beginning of the day, Machine A worked alone for 3 hours and completed \(\frac{1}{6}\) of a certain job.
Let Rate of Machine a = A, Rate of Machine B = B and Rate of Machien C = C
Rate * Time = Work
Time = 3
Work = 1/6
=> A * 3 = 1/6
=> A = 1/18
Machine A then worked together with Machine B for 2 hours, during which time \(\frac{1}{3}\) of the job was completed.
Combined Rate of A and B = A + B
=> (A + B) * 2 = 1/3
=> A + B = 1/6
=> 1/18 + B = 1/6 = 3/18
=> B = 2/18
Finally, Machine B and Machine C worked together for 4 hours and completed the remainder of the job.
Work Left = 1 = 1/6 - 1/3 = 6/6 - 1/6 - 2/6 = 3/6 = 1/2
Combined rate of B and C = B + C
=> (B + C) * 4 = 1/2
=> B + C = 1/8
=> 2/18 + C = 1/8
=> C = 1/8 - 1/9 = 1/72
How long would it have taken Machine C, working alone, to complete the job?
C * Time = 1
=> 1/72 * Time = 1
=> Time = 72
So, Answer will be E
Hope it Helps!
Watch following video to MASTER Work Rate Problems
Let Rate of Machine a = A, Rate of Machine B = B and Rate of Machien C = C
Rate * Time = Work
Time = 3
Work = 1/6
=> A * 3 = 1/6
=> A = 1/18
Machine A then worked together with Machine B for 2 hours, during which time \(\frac{1}{3}\) of the job was completed.
Combined Rate of A and B = A + B
=> (A + B) * 2 = 1/3
=> A + B = 1/6
=> 1/18 + B = 1/6 = 3/18
=> B = 2/18
Finally, Machine B and Machine C worked together for 4 hours and completed the remainder of the job.
Work Left = 1 = 1/6 - 1/3 = 6/6 - 1/6 - 2/6 = 3/6 = 1/2
Combined rate of B and C = B + C
=> (B + C) * 4 = 1/2
=> B + C = 1/8
=> 2/18 + C = 1/8
=> C = 1/8 - 1/9 = 1/72
How long would it have taken Machine C, working alone, to complete the job?
C * Time = 1
=> 1/72 * Time = 1
=> Time = 72
So, Answer will be E
Hope it Helps!
Watch following video to MASTER Work Rate Problems
