LM wrote:

Machines X and Y work at their respective constant rates. How many more hours does it take machine Y,working alone, to fill a prodcution order of a certain size than it takes machine X,workng alone?

( i ) Machines X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.

(ii) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does.

Let hx and rx be respectively the number of hours needed by machine x and its rate, and hy and ry the number of hours required by machine y and its rate.

To produce P, machines x and y require respectively hx and hy hours;

P = hx*rx = hy*ry => Ratio = hx/hy = ry/rx

(i) translates into : P = (rx+ry) * h = rx * h' = (rx+ry) * 2/3 * h'

hence Ratio = rx - 2/3 rx = 2/3 ry => ry /rx =2

(ii) translates into : P = ry * h = rx *h' = ry * 1/2 * h

hence : Ratio = ry/rx = 2

Both statements are enough to calculate that it takes twice more time to machine X for the same production.

What is teh OA ?

Cheers