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In the "Mashburn" pharmaceutical company there are two machi [#permalink]

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02 Oct 2012, 17:25

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In the "Mashburn" pharmaceutical company there are two machines - a machine that produces blue pills and a machine that produces red pills. The machines are operated 10 hours a day, and the daily quota of the "blue" machine is 20% greater than that of the red machine. If the "blue" machine was switched on at 8:00 and the "red" machine at 10:45, at what time will half of the combined daily quota be manufactured?

In the "Mashburn" pharmaceutical company there are two machines - a machine that produces blue pills and a machine that produces red pills. The machines are operated 10 hours a day, and the daily quota of the "blue" machine is 20% greater than that of the red machine. If the "blue" machine was switched on at 8:00 and the "red" machine at 10:45, at what time will half of the combined daily quota be manufactured?

a) 13:15 b) 14:15 c) 14:30 d) 15:40 e) 19:15

Thanks!

Say red machine's daily quota is 100 pills and blue machine's is 120 pills (20% greater), so total of 100+120=220 pills. Half of it would be 110 pills.

To fulfill daily quota red machine must produce 100/10=10 pills per hour and blue machine must produce 120/10=12 pills per hour.

Their combined rate, in this case, would be 10+12=22 pills per hour.

From 8:00 till 10:45, or in 11/4 hours, blue machine will produce 11/4*12=33 pills. After that together they must produce 110-33=77 pills. For that they will need 77/22=7/2 hours, or 3 hours and 30 minutes.

Therefore half of the combined daily quota will be manufactured at 10:45 + 3 hours and 30 minutes = 14:15.

Re: In the "Mashburn" pharmaceutical company there are two machi [#permalink]

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10 Jul 2013, 07:24

1

This post was BOOKMARKED

superpus07 wrote:

In the "Mashburn" pharmaceutical company there are two machines - a machine that produces blue pills and a machine that produces red pills. The machines are operated 10 hours a day, and the daily quota of the "blue" machine is 20% greater than that of the red machine. If the "blue" machine was switched on at 8:00 and the "red" machine at 10:45, at what time will half of the combined daily quota be manufactured?

a) 13:15 b) 14:15 c) 14:30 d) 15:40 e) 19:15

Thanks!

Blue machine(B) will complete its half in 5 hours, at 8:00 + 5 = 13:00 Hrs Red machine(R) will complete its half in 5 hours, at 10:45 + 5 = 15:45 Hrs

If we combine, B will first complete its work at 13:00 Hrs, then B and R will work together for remaining portion of 2:45 Hrs of work for R.

B is 20% efficient than R, so B = 1.2R R alone would complete the work in 2:45 Hrs = 11/4 Hrs R + 1.2R = 2.2R would complete the work in \(\frac{11}{4}*\frac{1}{2.2} = \frac{11}{4}*\frac{10}{22}=\frac{5}{4}=1:15 Hours\)

Time = 13:00 + 1:15 = 14:15 Hours
_________________

"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well." ― Voltaire Press Kudos, if I have helped. Thanks!

Re: In the "Mashburn" pharmaceutical company there are two machi [#permalink]

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26 Sep 2013, 22:44

I appreciate the problem at hand.

Since we need to calculate the 'half', we can consider that

Daily quota of Machine Red is 100 =>Daily quota of Machine Blue is 1.2(100)=120

Each operates for 10 hours a day, then

Rate = Daily quota/Daily operating hours

Rate(Blue)=12 Rate(Red) =10

Blue works till 10:45 alone and does 33 units of work. We have to complete half of (100+120) => 110 Remaining units = 77

Rate(Blue) + Rate (Red) = 22

Remaining Work/Rate = TIme

77/22=3.5 hours

10:45 + 3.5 hours = 14:15

Hope that helps !
_________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

In the "Mashburn" pharmaceutical company there are two [#permalink]

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25 Jul 2014, 03:28

In the "Mashburn" pharmaceutical company there are two machines - a machine that produces blue pills and a machine that produces red pills. The machines are operated 10 hours a day, and the daily quota of the "blue" machine is 20% greater than that of the red machine. If the "blue" machine was switched on at 8:00 and the "red" machine at 10:45, at what time will half of the combined daily quota be manufactured?

In the "Mashburn" pharmaceutical company there are two machines - a machine that produces blue pills and a machine that produces red pills. The machines are operated 10 hours a day, and the daily quota of the "blue" machine is 20% greater than that of the red machine. If the "blue" machine was switched on at 8:00 and the "red" machine at 10:45, at what time will half of the combined daily quota be manufactured?

13:15 14:15 14:30 15:40 19:15

Merging similar topics. Please refer to the discussion above.
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Re: In the "Mashburn" pharmaceutical company there are two machi [#permalink]

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09 Mar 2015, 06:21

1

This post was BOOKMARKED

Bunuel wrote:

superpus07 wrote:

In the "Mashburn" pharmaceutical company there are two machines - a machine that produces blue pills and a machine that produces red pills. The machines are operated 10 hours a day, and the daily quota of the "blue" machine is 20% greater than that of the red machine. If the "blue" machine was switched on at 8:00 and the "red" machine at 10:45, at what time will half of the combined daily quota be manufactured?

a) 13:15 b) 14:15 c) 14:30 d) 15:40 e) 19:15

Thanks!

Say red machine's daily quota is 100 pills and blue machine's is 120 pills (20% greater), so total of 100+120=220 pills. Half of it would be 110 pills.

To fulfill daily quota red machine must produce 100/10=10 pills per hour and blue machine must produce 120/10=12 pills per hour.

Their combined rate, in this case, would be 10+12=22 pills per hour.

From 8:00 till 10:45, or in 11/4 hours, blue machine will produce 11/4*12=33 pills. After that together they must produce 110-33=77 pills. For that they will need 77/22=7/2 hours, or 3 hours and 30 minutes.

Therefore half of the combined daily quota will be manufactured at 10:45 + 3 hours and 30 minutes = 14:15.

Answer: B.

Hope it's clear.

This approach is better and less time consuming than the approach that makes use of equations.

Great solution by Bunnel...Kudos!!!
_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time.

I hated every minute of training, but I said, 'Don't quit. Suffer now and live the rest of your life as a champion.-Mohammad Ali

Re: In the "Mashburn" pharmaceutical company there are two machi [#permalink]

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26 Mar 2015, 08:57

Bunuel wrote:

superpus07 wrote:

In the "Mashburn" pharmaceutical company there are two machines - a machine that produces blue pills and a machine that produces red pills. The machines are operated 10 hours a day, and the daily quota of the "blue" machine is 20% greater than that of the red machine. If the "blue" machine was switched on at 8:00 and the "red" machine at 10:45, at what time will half of the combined daily quota be manufactured?

a) 13:15 b) 14:15 c) 14:30 d) 15:40 e) 19:15

Thanks!

Say red machine's daily quota is 100 pills and blue machine's is 120 pills (20% greater), so total of 100+120=220 pills. Half of it would be 110 pills.

To fulfill daily quota red machine must produce 100/10=10 pills per hour and blue machine must produce 120/10=12 pills per hour.

Their combined rate, in this case, would be 10+12=22 pills per hour.

From 8:00 till 10:45, or in 11/4 hours, blue machine will produce 11/4*12=33 pills. After that together they must produce 110-33=77 pills. For that they will need 77/22=7/2 hours, or 3 hours and 30 minutes.

Therefore half of the combined daily quota will be manufactured at 10:45 + 3 hours and 30 minutes = 14:15.

Re: In the "Mashburn" pharmaceutical company there are two machi [#permalink]

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20 Jul 2016, 07:48

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In the "Mashburn" pharmaceutical company there are two machi [#permalink]

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20 Jul 2016, 20:24

Top Contributor

superpus07 wrote:

In the "Mashburn" pharmaceutical company there are two machines - a machine that produces blue pills and a machine that produces red pills. The machines are operated 10 hours a day, and the daily quota of the "blue" machine is 20% greater than that of the red machine. If the "blue" machine was switched on at 8:00 and the "red" machine at 10:45, at what time will half of the combined daily quota be manufactured?

A. 13:15 B. 14:15 C. 14:30 D. 15:40 E. 19:15

In 10 hrs the blue machine does 6/11 of the work. So from 8 to 10:45 i.e, in 11/4 hrs it does 6/40 of the work 1/2 of the work is to be done. So remaining work is 1/2 - 6/40 = 7/20 Together blue and red machine does 1/10 of the work in 1 hr. They will do 7/20 of the work in 3.5 hrs So work will be completed in 10:45 + 3.5 hrs = 14:15
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