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Working alone at their respective constant rates, machine A and machin

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Aaditya96
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Working alone at their respective constant rates, machine A and machin [#permalink] New post   21 Jul 2019, 06:35
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Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively. If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill 1/2 of that order?

A: 1/2

B: 3/4

C: 1

D: 1 1/4

E: 1 1/2
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C
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NandishSS
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Re: Working alone at their respective constant rates, machine A and machin [#permalink] New post   21 Jul 2019, 07:06
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Aaditya96 wrote:
Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively. If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill 1/2 of that order?

A: 1/2

B: 3/4

C: 1

D: 1 1/4

E: 1 1/2


machine A and machine B can fill a certain order in 3 hours and 6 hours

Together can fill in \(1/3+1/6 = 1/2\) i,e 2 hours, However, if two machines to fill 1/2 of that order = 1 hour

Hence C
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Re: Working alone at their respective constant rates, machine A and machin [#permalink] New post   29 Dec 2019, 18:39
NandishSS wrote:
Aaditya96 wrote:
Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively. If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill 1/2 of that order?

A: 1/2

B: 3/4

C: 1

D: 1 1/4

E: 1 1/2


machine A and machine B can fill a certain order in 3 hours and 6 hours

Together can fill in \(1/3+1/6 = 1/2\) i,e 2 hours, However, if two machines to fill 1/2 of that order = 1 hour

Hence C


Could you try answering this using the rate time work table? I can't make out how you solved this question.

I plugged in a multiple of 6 and 3 for the work table and solved for each respective rate. I then used the new rate and work to solve for the time spent, but keep getting 2 1/4 hrs not 1. Any tips?

For example:

Machine Rate Time Work
Alone A 24/3= 8 3 hrs 24 lbs
Alone B 24/6= 4 6 hrs 24 lbs
Working Simultaneously
A 8 3/4 hrs 6 lbs
B 4 1.5 hrs 6 lbs

2 1/4 hrs = time spent with A + B working simultaneously to generate 12 lbs (1/2 work)
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If a portion of a half water/half alcohol mix is replaced with 25% [#permalink] New post   Updated on: 11 Jul 2021, 06:35
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Aaditya96 wrote:
Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively. If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill 1/2 of that order?

A: 1/2
B: 3/4
C: 1
D: 1 1/4
E: 1 1/2


Another approach is to assign a "nice value" to the job.
That is, a value that works well with the given information of 3 hours and 6 hours
So let's say the order consists of making 18 widgets

Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively
In other words, Machine A can make 18 widgets in 3 hours, which means Machine A's RATE = 6 widgets per hour
This also tells us that Machine B can make 18 widgets in 6 hours, which means Machine B's RATE = 3 widgets per hour

If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill 1/2 of that order?
COMBINED rate = 6 + 3 = 9 widgets per hour

We want to fill 1/2 the order.
1/2 of 18 widgets is 9 widgets
So we want to make 9 widgets

time = output/rate
So, time = 9/9 = 1 hour

Answer: C

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 06 Apr 2020, 10:34.
Last edited by BrentGMATPrepNow on 11 Jul 2021, 06:35, edited 1 time in total.
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Re: Working alone at their respective constant rates, machine A and machin [#permalink] New post   08 Jul 2021, 05:27
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Aaditya96 wrote:
Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively. If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill 1/2 of that order?

A: 1/2

B: 3/4

C: 1

D: 1 1/4

E: 1 1/2


Solution -


The rate at which Machine A alone can fill the order = \(\frac{1}{3\\
}\)

The rate at which Machine B alone can fill the order = \(\frac{1}{6}\)

The rate at which both Machine A and Machine B together can fill the order = \(\frac{1}{3}+ \frac{1}{6}= \frac{3}{6} =\frac{1}{2} \\
\)

So, the time taken by Machine A and Machine B together to fill the order is 2 hours.

Therefore, the time taken by both the machines to fill half of the order is 1 hour.

So, the best answer is C.
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Re: Working alone at their respective constant rates, machine A and machin [#permalink] New post   06 Nov 2022, 01:27
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Re: Working alone at their respective constant rates, machine A and machin [#permalink]
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