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Working alone at its constant rate, machine A can complete a job in 24
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03 May 2021, 10:37
03 May 2021, 10:37
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Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A. If machine A works on the job for 6 hours and machine B completes the job, how long does it take machine B to finish the job?
A. 12hrs
B. 16hrs
C. 24hrs
D. 32hrs
E. 36hrs
A. 12hrs
B. 16hrs
C. 24hrs
D. 32hrs
E. 36hrs
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Joined: 10 Apr 2015
Posts: 6218
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Re: Working alone at its constant rate, machine A can complete a job in 24
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03 May 2021, 12:45
03 May 2021, 12:45
2
Carcass wrote:
Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A. If machine A works on the job for 6 hours and machine B completes the job, how long does it take machine B to finish the job?
A. 12hrs
B. 16hrs
C. 24hrs
D. 32hrs
E. 36hrs
A. 12hrs
B. 16hrs
C. 24hrs
D. 32hrs
E. 36hrs
Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A.
So, it must take Machine B 48 hours to complete the job.
Now let's assign a nice value to the job. That is, we'll assign a value that works well with 24 hours and 48 hours.
Let's say that the entire job consists of making a total of 48 widgets
If it take Machine A 24 hours to make 48 widgets, then machine A's RATE = 2 widgets per HOUR
If it take Machine B 48 hours to make 48 widgets, then machine B's RATE = 1 widget per HOUR
If machine A works on the job for 6 hours . . .
At a rate of 2 widgets per HOUR, machine A can make 12 widgets in 6 hours
So, the amount of work remaining = 48 widgets - 12 widgets = 36 widgets
. . . and machine B completes the job, how long does it take machine B to finish the job?
Machine B must make the 36 widgets
Machine B's RATE = 1 widget per HOUR
Time = output/rate = 36/1 = 36
It will take machine B 36 hours to complete the job.
Answer: E
Cheers,
Brent
Re: Working alone at its constant rate, machine A can complete a job in 24
[#permalink]
29 Jan 2022, 10:46
29 Jan 2022, 10:46
How did we arrive at 48hours for machine B?
Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A.
So, it must take Machine B 48 hours to complete the job.
Now let's assign a nice value to the job. That is, we'll assign a value that works well with 24 hours and 48 hours.
Let's say that the entire job consists of making a total of 48 widgets
If it take Machine A 24 hours to make 48 widgets, then machine A's RATE = 2 widgets per HOUR
If it take Machine B 48 hours to make 48 widgets, then machine B's RATE = 1 widget per HOUR
If machine A works on the job for 6 hours . . .
At a rate of 2 widgets per HOUR, machine A can make 12 widgets in 6 hours
So, the amount of work remaining = 48 widgets - 12 widgets = 36 widgets
. . . and machine B completes the job, how long does it take machine B to finish the job?
Machine B must make the 36 widgets
Machine B's RATE = 1 widget per HOUR
Time = output/rate = 36/1 = 36
It will take machine B 36 hours to complete the job.
Answer: E
Cheers,
Brent
GreenlightTestPrep wrote:
Carcass wrote:
Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A. If machine A works on the job for 6 hours and machine B completes the job, how long does it take machine B to finish the job?
A. 12hrs
B. 16hrs
C. 24hrs
D. 32hrs
E. 36hrs
A. 12hrs
B. 16hrs
C. 24hrs
D. 32hrs
E. 36hrs
Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A.
So, it must take Machine B 48 hours to complete the job.
Now let's assign a nice value to the job. That is, we'll assign a value that works well with 24 hours and 48 hours.
Let's say that the entire job consists of making a total of 48 widgets
If it take Machine A 24 hours to make 48 widgets, then machine A's RATE = 2 widgets per HOUR
If it take Machine B 48 hours to make 48 widgets, then machine B's RATE = 1 widget per HOUR
If machine A works on the job for 6 hours . . .
At a rate of 2 widgets per HOUR, machine A can make 12 widgets in 6 hours
So, the amount of work remaining = 48 widgets - 12 widgets = 36 widgets
. . . and machine B completes the job, how long does it take machine B to finish the job?
Machine B must make the 36 widgets
Machine B's RATE = 1 widget per HOUR
Time = output/rate = 36/1 = 36
It will take machine B 36 hours to complete the job.
Answer: E
Cheers,
Brent
