# Math Competition Problems - Problem of the Week - 20

Updated: Jun 17, 2021

Andrew is doing some tidying. He can tidy 2 big rooms in the same time it takes to tidy 3 small rooms. He can tidy one big room and three small rooms in 90 minutes. How long will it take him to tidy 3 big rooms and 6 small rooms? - AMC (Australian Mathematical Competition) Upper Primary 2018, Question 20

Let a big circle represent the time taken to tidy a big room.

Let a small circle represent the time taken to tidy a small room

Since he can tidy 2 big rooms at the same time as 3 small rooms,

2 big circles = 3 small circles

He can tidy 1 big room and 3 small rooms in 90 mins.

So, 1 big circle + 3 small circles = 90 mins

We can **replace the 3 small circles with 2 big circles** because they are equivalent.

Hence our equation becomes 3 big circles = 90 mins

**Hence one big circle has to be 30 mins. Which means he takes 30 mins to clean the big room**

Since,

We can **replace the big circle with 30** and get

30 + 3 small circles = 90

So we know the 3 small circles have to be 60.

**Which means 1 small circle = 20. So he takes 20 minutes to tidy a small room.**