Machine $A$ produces pencils at a constant rate of $9000$ pencils per hour, and machine $B$ produces pencils at

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sun Dec 12, 2021 1:42 am

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Machine $A$ produces pencils at a constant rate of $9000$ pencils per hour, and machine $B$ produces pencils at a constant rate of $7000$ pencils per hour. If the two machines together must produce $100,000$ pencils and if each machine can operate for at most $8$ hours, what is the least amount of time, in hours, that machine $B$ must operate?

A. $4$

B. $4 \frac23$

C. $5\frac13$

D. $6$

E. $6 \frac14$

Answer: A

Source: GMAT Paper Tests

Source: Beat The GMAT — Problem Solving | Sun Dec 12, 2021 1:42 am

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Re: Machine $A$ produces pencils at a constant rate of $9000$ pencils per hour, and machine $B$ produces pencils a

by Brent@GMATPrepNow » Mon Dec 13, 2021 7:04 am

Gmat_mission wrote: ↑
Sun Dec 12, 2021 1:42 am
Machine $A$ produces pencils at a constant rate of $9000$ pencils per hour, and machine $B$ produces pencils at a constant rate of $7000$ pencils per hour. If the two machines together must produce $100,000$ pencils and if each machine can operate for at most $8$ hours, what is the least amount of time, in hours, that machine $B$ must operate?

A. $4$

B. $4 \frac23$

C. $5\frac13$

D. $6$

E. $6 \frac14$

Answer: A

Source: GMAT Paper Tests

To MINIMIZE machine B's operating time, we must MAXIMIZE the time machine A's operating time.
So, let machine A operate for the full 8 hours.
In 8 hours, machine A produces 72,000 pencils [8 hours x 9,000 pencils/hour =72,000 pencils]

So, the number of pencils machine B must make = 100,000 - 72,000 = 28,000

Time = output/rate
So, operating time = 28,000/7000 = 4 hours

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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