20 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 ?
from the question you know that 21 r = 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 27 r = 1 / 7 , therefore 6 more machines ! d
subtract(divide(multiply(20, 9), subtract(9, const_2)), 20)