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01 Feb 2024, 02:30
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Machine A can complete a job in 12 hours and has worked for 4 hours on it. Machine B operates at a rate that is 2/3 of machine A's rate. How many more hours does machine B need to work alone to finish the remaining part of the job?
A. 12 hrs
B. 16 hrs
C. 24 hrs
D. 28 hrs
E. 32 hrs
A. 12 hrs
B. 16 hrs
C. 24 hrs
D. 28 hrs
E. 32 hrs
Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone?
01 Feb 2024, 03:36
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Using the percent approach presented on the Tips and Hints post (https://gmatclub.com/forum/tips-and-hin ... 72096.html) we assume that the task is 100%
A does 100% of the job in 12 hours (100work/12hours). After 4 hours, machine A would have completed aprox 33% of the job (12x = 100*4; x= 33% work)
B does 100% of the job at a rate that is 2/3 of machine´s A rate. This means, machine B es SLOWER than machine A.
Use the reciprocal to understand machine B work rate -- 3/2 of 12 = 18 hours. Hence, machine B does 100% of the job in 18 hours (100work/18hrs).
How many minutes does machine B take to complete the remaining aprox 67% of the job? (100%-33% that has already been completed by machine A)?
100x = 67*18; x = 1206/100; x= 12 hours (rounding)
Solution: 12 hours
Hope it helps!
A does 100% of the job in 12 hours (100work/12hours). After 4 hours, machine A would have completed aprox 33% of the job (12x = 100*4; x= 33% work)
B does 100% of the job at a rate that is 2/3 of machine´s A rate. This means, machine B es SLOWER than machine A.
Use the reciprocal to understand machine B work rate -- 3/2 of 12 = 18 hours. Hence, machine B does 100% of the job in 18 hours (100work/18hrs).
How many minutes does machine B take to complete the remaining aprox 67% of the job? (100%-33% that has already been completed by machine A)?
100x = 67*18; x = 1206/100; x= 12 hours (rounding)
Solution: 12 hours
Hope it helps!
Rate of A= 1/12
Rate of B= 2/3 * 1/12 =1/18
Therefore,
(Ra)*Time + (Rb)*time(b)=1
(1/12)*4 + (1/18)* time(b)=1
(1/18)*time(b)= 2/3
Therefore time(b)= Time taken by B to complete remaining work alone= (2/3)*18 = 12 Hrs
Rate of B= 2/3 * 1/12 =1/18
Therefore,
(Ra)*Time + (Rb)*time(b)=1
(1/12)*4 + (1/18)* time(b)=1
(1/18)*time(b)= 2/3
Therefore time(b)= Time taken by B to complete remaining work alone= (2/3)*18 = 12 Hrs
