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May 19th, 2017, 12:56 AM   #1
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Ratio & Proportion

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
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May 19th, 2017, 01:34 AM   #2
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There's 3 times as much work (12 rooms instead of 4) and 3 times as many people to do it (9 instead of 3), so of course it will take the same amount of time, 30 minutes.

The 'same rate' just means the workers aren't changing the speed at which they clean the rooms.
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