Machine M, working alone at its constant rate, produces x widgets every 4 minutes. Machine N, working alone at its constant rate, produces y widgets every 5 minutes. If machines M and N working simultaneously at their respective constant rates for 20 minutes, does machine M produce more widgets than machine N in that time?

(1) x > 0.8y

(2) y = x + 1

Step-by-step explanation: Machine M produces X widgets every 4 minutes

Machine N produces Y widgets every 5 minutes.

so, in 20 minutes of simultaneous work, which machine will produce more widgets?

in 20 minutes of work machine M produces 5*X widgets, because 20/4 = 5

and in this time machine N produces 4*Y widgets, because 20/5 = 4

1) x > 0.8y.

So if we want to know if machine M produces more than machine N, we need to see if 5*X is greater than 4*Y.

as X> 0.8Y we know that X = 0.8*Y is a lower limit of X.

then if we replace it into the equation 5*X = 5*4/5*Y = 4*Y, so in the lower limit both machines produce the same widgets, but X>4/5*Y, then for all this set, machine M produces more than machine N

2) y = x + 1.

if we put this in the equation; then machine N produces 4*Y = 4*X + 4

so machine M produces 5*X and machine N produces 4*X + 4.

equaling them, we get 5*X = 4*X + 4

5*X - 4*X - 4 = X - 4 = 0, so if X = 4, both machines produce the same amount of widgets. If X 4, machine M produces more.