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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? 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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03 Oct 2012, 03:27
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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 11033=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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25 Oct 2012, 07:00
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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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 810:45 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 11033 = 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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Re: In the "Mashburn" pharmaceutical company there are two machi [#permalink]
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10 Jul 2013, 07:24
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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, 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?
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, 03:34



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Re: In the "Mashburn" pharmaceutical company there are two machi [#permalink]
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09 Mar 2015, 06:21
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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 11033=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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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 11033=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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20 Jul 2016, 18:08
combined hourly quota=1.2+1=2.2 units combined daily quota=10*2.2=22 units let t=time 1.2*t+1*(t2.75)=22/2=11 units t=6.25 hours 14:15
Last edited by gracie on 24 Jul 2016, 17:51, 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, 20:24
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, 20:41
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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