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 2 x units of product p in 3 days ?
"4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 2 x units in 3 days therefore , we need to get to 2 x / 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 2 x done in 3 days . 2 x / 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 = 2 x / 3 y = 2 x / 3 * 24 / x cancel 3 with 24 , and x with x and get - > 16 . answer choice c"
multiply(multiply(4, 2), divide(6, 3))