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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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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
[Reveal] Spoiler: OA
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03 Oct 2012, 02:27
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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!

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.

Hope it's clear.
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Re: In the "Mashburn" pharmaceutical company there are two machi [#permalink]

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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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14 Nov 2012, 01:10
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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

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

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10 Jul 2013, 02:58
Bumping for review and further discussion.
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Re: In the "Mashburn" pharmaceutical company there are two machi [#permalink]

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10 Jul 2013, 06:24
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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

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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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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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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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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09 Mar 2015, 05:21
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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.

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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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.

Hope it's clear.

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

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20 Jul 2016, 06:48
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In the "Mashburn" pharmaceutical company there are two machi [#permalink]

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20 Jul 2016, 17:08
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

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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20 Jul 2016, 19:24
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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In the "Mashburn" pharmaceutical company there are two machi [#permalink]

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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

Thanks,
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In the "Mashburn" pharmaceutical company there are two machi   [#permalink] 23 Jul 2016, 19:41
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