Math Competition Problems - Problem of the Week - 20

Updated: Jun 17

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.





So Andrew takes 30 minutes to tidy 1 Big Room

and 20 minutes to tidy 1 Small Room.


We know it is right because time taken for 2 big rooms is 30*2=60 and time taken for 3 small rooms is 20*3=60 and they are equal.


Which means for 3 big rooms it will take him 90 minutes and 6 small rooms it will take him 120 minutes, giving a total of 210 minutes or 3 hours and 30 minutes.


Want to prepare for AMC? Working out the problems by yourself is the only way to prepare for it.


Try out a similar problem.

5 Oranges cost the same as 4 Apples. If 4 Apples and 4 Oranges cost $5.40, then how much does 5 Oranges and 3 Apples cost?

5 Oranges cost the same as 4 Apples. If 4 Apples and 4 Oranges cost $5.40, then how much do 5 Oranges and 3 Apples cost?
Interesting Math Problem 113

Get your brains working and write your answers in the comments section below.


Did you like the problem? Would you like to have these problems and solutions delivered to your inbox as I publish them? Click here to subscribe

#Competition, #Math #Problems #OnlineMathEnrichmentPrograms #ProblemOfTheWeek #AMCPrep #AustralianMathematicalCompetition #Grade5 #Grade6 #AustralianMathematicsCompetition #MathCompetitionsPreparation

Previous Week's Problem

Problem of the Week 19

Next Week's Problem

Problem of the Week 21