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

B. 18

Step-by-step explanation:

The 4 machines can produce x units in 6 days. This means they have a daily total rate of x/6 units per day.

Since the machines are similar and that they work at the same rate, this means that the individual rates of each machine would be x/6/4 = x/24 units per day.

Now we are looking at producing 3x units in 4 days. This means that we want to produce 3x/4 units in a single day. Now, since each machine would work at a rate of x/24, we need to know the number of machines we need. To know this number, we simply divide what is to be achieved by the individual rate:

This is 3x/4 divided by x/24. This mathematically means 3x/4 * 24/x = 18 machines

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