BTGmoderatorDC wrote:Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8
Use the following equation:
(machines)(time) / output = (machines)(time) / output
In the equation above:
Machines and time are INVERSELY PROPORTIONAL.
As the number of machines increases, the amount of time required to produce the same output decreases.
Machines and output are DIRECTLY PROPORTIONAL.
As the number of machines increases, the amount of output also increases.
Time and output are also DIRECTLY PROPORTIONAL.
As the amount of time increases, the amount of output also increases.
Let x=1.
Since 4 machines take 6 days to produce x=1 unit, and we want to know how many machines are required to produce 3x=3 units in 4 days, we get:
(4 machines)(6 days)/(1 unit) = (n machines)(4 days)/(3 units)
24 = 4n/3
72 = 4n
18 = n
The correct answer is
B.
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