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 6 days?	Pick.
A) 24  B) 18  C) 16  D) 12  E) 8

Rationale: "4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 4 x units in 6 days therefore , we need to get to 4 x / 6 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 3 x done in 6 days . 3 x / 6 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 3 x / 6 y = 3 x / 6 * 24 / x cancel 6 with 24 , and x with x and get - > 12 . answer choice d"
Answer: D