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In the "Mashburn" pharmaceutical company there are two machi

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

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New post 02 Oct 2012, 16:25
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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?

A. 13:15
B. 14:15
C. 14:30
D. 15:40
E. 19:15
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Re: In the "Mashburn" pharmaceutical company there are two machi  [#permalink]

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New post 03 Oct 2012, 02:27
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4
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.
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Re: In the "Mashburn" pharmaceutical company there are two machi  [#permalink]

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New post 25 Oct 2012, 06:00
very tricky question:

let the total reb be 100 and blue be 120( 20% greater)

so half will be 120 +100 /2 = 110

per hour by blue = 12 so in 2hrs 45 mins it will be 33( or at 10:45) so balance is 110 -33 = 77

per hr by red is 10 so from 10:45 combined will be 12+10 =22 /hr

by 1 :45 it will be 99
then by 2:15 (22/2) 99 +11 = 110

So By 2:45 it will complete.
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Re: In the "Mashburn" pharmaceutical company there are two machi  [#permalink]

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New post 14 Nov 2012, 01:10
1
Rate of Blue = \(\frac{1.2x}{10}\)
Rate of Red = \(\frac{x}{10}\)

Let x = 100

\(Rate of Blue = \frac{120}{10}=\frac{12}{1 hr}\)
\(Rate of Red = \frac{100}{10}=\frac{10}{1 hr}\)

Quota for 10 hours or 1 day: 220 (combined)
Half the quota: 110

If Blue machine runs from 8-10:45 which is \(2\frac{3}{4}=\frac{11}{4}hrs\)
Rt = W
\(\frac{12}{1hr}x\frac{11}{4}=33\)

How many hours more to produce 110-33 = 77 by two machines now running together?

\(\frac{22}{1hr}=\frac{77}{t}\)
t=3.5 hrs

Answer: 14:15
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Re: In the "Mashburn" pharmaceutical company there are two machi  [#permalink]

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New post 10 Jul 2013, 02:58
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Re: In the "Mashburn" pharmaceutical company there are two machi  [#permalink]

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New post 10 Jul 2013, 06:24
1
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
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Re: In the "Mashburn" pharmaceutical company there are two machi  [#permalink]

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New post 26 Sep 2013, 21:44
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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New post 25 Jul 2014, 02:28
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?

13:15
14:15
14:30
15:40
19:15
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Re: In the "Mashburn" pharmaceutical company there are two machi  [#permalink]

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New post 25 Jul 2014, 02:34
goodyear2013 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?

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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New post 09 Mar 2015, 05:21
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!!!
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Re: In the "Mashburn" pharmaceutical company there are two machi  [#permalink]

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New post 26 Mar 2015, 07:57
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.

Answer: B.

Hope it's clear.






Thanks for the solution.
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In the "Mashburn" pharmaceutical company there are two machi  [#permalink]

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New post Updated on: 24 Jul 2016, 16:51
combined hourly quota=1.2+1=2.2 units
combined daily quota=10*2.2=22 units
let t=time
1.2*t+1*(t-2.75)=22/2=11 units
t=6.25 hours
14:15

Originally posted by gracie on 20 Jul 2016, 17:08.
Last edited by gracie on 24 Jul 2016, 16:51, edited 1 time in total.
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In the "Mashburn" pharmaceutical company there are two machi  [#permalink]

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New post 20 Jul 2016, 19:24
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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


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

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New post 23 Jul 2016, 19:41
I prefer listing the complete equation (Rate*Time=Work) when solving such Work problems.

Regarding the production proportion, let's pick "Smart Numbers":
The company produces 12 blue pills and 10 red pills.

We use B referring to the rate of producing blue pills and R to that of producing red pills.

Based on the identical 10 hours, B=1.2 and R=1

Time for B is 3.75 hours longer than for R, and T represents the time we want.

To produce half of the combined quota, we establish the equation as below:
1.2*(T+2.75)+1*T=11
T=3.5

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

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New post 18 Aug 2017, 16:12
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.
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Re: In the "Mashburn" pharmaceutical company there are two machi  [#permalink]

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New post 07 Sep 2018, 16:17
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


Let the daily quota for the red machine be 100 pills, so the daily quota for the blue machine is 120 pills. Thus, the combined daily quota is 220 pills.

Since each machine is operated 10 hours a day, the rate of the red machine is 10 pills per hour and the rate of the blue machine is 12 pills per hour. So their combined rate is 22 pills per hour. Therefore, they need to produce a total of 110 pills to satisfy half of the combined daily quota. However, since the blue machine has worked 2 hour 45 minutes before the red machine does, the blue machine has produced 2.75 x 12 = 33 pills. Therefore, when they work together starting at 10:45, they need to produce only 110 - 33 = 77 pills. We can create the following equation where t = the number of hours they work together to produce 77 pills:

22t = 77

t = 77/22 = 7/2 = 3.5

So they will produce half of the combined daily quota by 10:45 + 3.5 hours = 10:45 + 3:30 = 13:75 = 14:15.

Answer: B
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