Ratio Proportion: it takes 30 minutes for 3 people to clean four identical rooms.

could somebody help me with this question:-

it takes 30 minutes for 3 people to clean four identical rooms. How long would it take 9 people to clean 12 of the same rooms at the same rate

I find he Phrase "Same rate" confusing. My answer is 30 minutes but my teacher says it is 90 minutes and I can't understand why

This is how I did it:-

3 People = 4 rooms in 30 minutes

Divide LHS by 3 and multiply RHS with 3

1 People = 4 rooms in 90 minutes

multiply LHS by 9 and Divide RHS with 9

9 People = 4 rooms in 10 minutes

Multiply RHS with 3

9 People = 12 rooms in 30 minutes

Answer 30 Minutes