Math Competition Problems - Problem of the Week - 20

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.