It would take machine Z 13.5 minutes to produce the same number of items.
Step-by-step explanation:
Step 1:
If machine y produces 3 items in the same time that machine z produces 2 items, we can create a ratio as follows;
[tex]\frac{y}{3} : \frac{z}{2}[/tex], this represents the above statement.
If we divide this by 2 we get,
[tex]\frac{y}{1.5} : \frac{z}{1}[/tex] this means if y takes 1 minute to do a particular task it would take 1.5 times that for z to do the same.
Step 2:
To calculate how long it would take machine z to do something that machine y does in 9 minutes, we multiply 1.5 with the time y takes i.e. 9 minutes.
[tex]9(1.5)= 13.5,[/tex] so it would take machine z 13.5 minutes to produce the same number of items.
