Twenty one 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 two days? Choose the correct choice
A) 2 B) 3 C) 4 D) 6 E) 9
From the question you know that 21R = 1/9. The question asks you (partially) to make the rate from 1/9 to 1/7 (drop from 9 day to 7). So the only thing that you need to do is to find the magic number than can convert 1/9 to 1/7.   So 1/9 * x = 1/7 (1 equation with one unknown). So by solving this you get x = 9/7 . Thats it then! Take the magic number 9/7 and multiply BOTH sides of the original equation and you have:   21*(9/7)*R = (9/7) * 1/9   27* R = 1/7, Hence 27R = 1/7, therefore 6 more machines!   6
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Twenty one 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 two days?