algebra 1b unit 4

Question

I can clean my whole kitchen in (on average) 20 minutes. My daughter takes (on average) 30 minutes to do the same job. If I ask her to help me, how many minutes will it take us to clean the kitchen together (as long as we cooperate)? 

25

14.5

12

10.3

None of the above

Answer 1

Let x = number of minutes that it takes for both to do the job

Portion done by mom per minute = 1/20

Portion done by daughter per minute = 1/30

Portion done by both per minute = 1/x

Then, 1/x = 1/20 + 1/30

Multiply by 60x to get 60 = 3x + 2x

So, 5x = 60

x = 12

It takes 12 minutes to clean the kitchen when both people are working together.