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word problem - machines -- different concept

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word problem - machines -- different concept

by hpgmat » Fri Nov 13, 2009 3:59 pm
Machine A produces pencils at constant rate of 9000 pencils per hour and machine B produces pencils at constant rate of 7000 pencils per hour . if the two machines together must produce 100000 pencils and if each machine cna operate for at most 8 hours , what is the least amount of time , in hours that machine B must operate ?

A)4
B)4-2/3
C)5-1/3
D)6
E)6-1/4

please show calculations.
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Re: word problem - machines -- different concept

by Stuart@KaplanGMAT » Fri Nov 13, 2009 4:40 pm
hpgmat wrote:Machine A produces pencils at constant rate of 9000 pencils per hour and machine B produces pencils at constant rate of 7000 pencils per hour . if the two machines together must produce 100000 pencils and if each machine cna operate for at most 8 hours , what is the least amount of time , in hours that machine B must operate ?

A)4
B)4-2/3
C)5-1/3
D)6
E)6-1/4

please show calculations.
Machine A produces pencils quicker than Machine B. Since we want to minimize the total amount of run time for B, let's maximize the total run time for A.

We're told max time per machine is 8 hours. In 8 hours, Machine A can produce 8*9000 = 72000 pencils.

We want 100000 pencils, so machine B must produce 100000-72000=28000 pencils.

28000 pencils at 7000 pencils/hour = 28000/7000 = 4 hours... choose A.

This question is another good illustration of the general principle that whenever you want to minimize one thing, you usually maximize something else.
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