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# Six machines, each working at the same constant rate,

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Manager
Joined: 22 Aug 2006
Posts: 139
Followers: 1

Kudos [?]: 1 [0], given: 0

Six machines, each working at the same constant rate, [#permalink]  19 Nov 2006, 22:09
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Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

A. 2
b. 3
c. 4
d. 6
e. 8

Manager
Joined: 03 Jul 2005
Posts: 194
Location: City
Followers: 1

Kudos [?]: 5 [0], given: 0

Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

A. 2
b. 3
c. 4
d. 6
e. 8

6 * 12 = 72 (Time it would take one machine)

72days divided by 8 days = 9 machines

9 machines less 6 machines = 3 machines

.
Director
Joined: 05 Feb 2006
Posts: 902
Followers: 1

Kudos [?]: 51 [0], given: 0

Yeah use the simple formula:

1/r+1/r+1/r+1/r+1/r+1/r=1/12

6/r=1/12
r=72 (rate of each machine)

Asks how many additional machines will be needed, calculated how many in total will be needed:

x/72=1/8
8x=72
x=9 (machines)

9-6=3

B
Director
Joined: 28 Dec 2005
Posts: 922
Followers: 2

Kudos [?]: 37 [0], given: 0

Agree with 3.

If x is the rate:
6*(1/x) = 1/12
=>x = 72, 1 machine will take 72 days to complete the job

if y is number of additional machines:

(6+y)/72 = 1/8 => y=3
Senior Manager
Joined: 08 Jun 2006
Posts: 342
Location: Washington DC
Followers: 1

Kudos [?]: 23 [0], given: 0

6 * 12 = n * 8 => n = 9
Additional machines = 9-6 = 3
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