machines !

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charmaine: Senior | Next Rank: 100 Posts; Posts: 71; Joined: Sun May 18, 2008 11:04 pm; Thanked: 1 times

machines !

by charmaine » Sun Sep 21, 2008 5:29 pm

Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, to complete the job is 16 hours. How many hours would be needed if only 8 of the machines, working together, were used to complete the job?

(A) 18
(B) 20
(C) 22
(D) 24
(E) 26

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Source: Beat The GMAT — Problem Solving | Sun Sep 21, 2008 5:29 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pm; Thanked: 331 times; Followed by:11 members

by cramya » Sun Sep 21, 2008 6:03 pm

Rate of 1 machine * no of machines * time = 1 job

Rate of 1 machine *10 * 16 = 1

Rate of 1 machine = 1/160

using the rate of 1 machine above and the same formula

1/160*8*time = 1
time = 160/8 = 20

Another approach is:

no of machines*time = no of machines * time
10*16 = 8*x
x=20

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b.kurland: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Mon Jul 14, 2008 2:52 pm; GMAT Score:720

by b.kurland » Sun Sep 21, 2008 6:06 pm

i say B)20
i arrived at this answer by using an arbitrary value for the # of products being made.
let's say the machines are making pens, and since there are 10 machines and 16 hours, 160 pens seems like a good number to shoot for.
so if 10 machines work 16 hours to make 160 pens, then their combined per hour rate is 10 pens/hr. and, since there are ten machines, the hourly rate per machine is 1 pen/hr.
now, you're told that only 8 machines are making pens. the individual rate for each machine remains the same (1 pen/hr), so 8 machines each making 1 pen per hour means that the combined hourly rate is 8 pens/hr.
at this point, just apply the formula rate*time=distance, or in this case, r*t=pens. the 8 machines have to make 160 pens, and the rate of these 8 machines working together is 8 pens/hr, so the formula given these values is (8 pens/hr)(time)=160 pens...t=160/8, or 20 hours.
if you're looking for a purely algebraic explanation, well, you can derive it from everything i said

. hope this helps