Twelve identical machines, running continuously at the same constant rate, take 9 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by three days?  Choose the correct choice
A) 2  B) 3  C) 4  D) 6  E) 9
From the question you know that 12R = 1/9. The question asks you (partially) to make the rate from 1/9 to 1/6 (drop from 9 day to 6). So the only thing that you need to do is to find the magic number than can convert 1/9 to 1/6.   So 1/9 * x = 1/6 (1 equation with one unknown). So by solving this you get x = 9/6 or 3/2. Thats it then! Take the magic number 4/3 and multiply BOTH sides of the original equation and you have:   12*(3/2)*R = (3/2) * 1/9   6 * 3 * R = 1/6, Hence 18R = 1/6, therefore 6 more machines!   6
<result>D</result>
Twelve identical machines, running continuously at the same constant rate, take 9 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by three days?