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 2x units of product P in 3 days? Choose the correct choice from the following options
A) 24
B) 18
C) 16
D) 12
E) 8
4 machines do x units in 6 days   we have x/6 =&gt; rate of the 4 machines   we know that we need to have 2x units in 3 days   therefore, we need to get to 2x/3 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 2x done in 3 days.   2x/3 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 = 2x/3   y = 2x/3 * 24/x   cancel 3 with 24, and x with x and get -&gt; 16. Answer choice 16
<result>C</result>
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 2x units of product P in 3 days?