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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]  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

Thanks!
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Re: In the "Mashburn" pharmaceutical company there are two machi [#permalink]  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 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]  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]  14 Nov 2012, 02:10
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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

Re: In the "Mashburn" pharmaceutical company there are two machi   [#permalink] 14 Nov 2012, 02:10
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