Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same amount of time in which machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take machine Z to produce the same number of items

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;

, this represents the above statement.

If we divide this by 2 we get,

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.

so it would take machine z 13.5 minutes to produce the same number of items.