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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

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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 !
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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 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
_________________

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

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18 Aug 2017, 17:12

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.

Thanks for sharing the solution Bunuel. I was able to solve the question but with all equations and variables. :(

Assuming "100" here as Red pills production made the calculation very simple. 100 or 10s multiple is first assumption which comes in my head but doesn't work in all questions. Do you have any suggestions where I can learn or get logic on estimation of numbers to ease the calculation and save time.