SOLUTION: Hannah and Lindsay clean an office. Hannah can clean the office alone in 3 hours. While Lindsay can in 2 hours. HOw long will it take them if they work together?

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Question 1008104: Hannah and Lindsay clean an office. Hannah can clean the office alone in 3 hours. While Lindsay can in 2 hours. HOw long will it take them if they work together?
Found 3 solutions by noahjavierwilliams43, ikleyn, cparks1000000:
Answer by noahjavierwilliams43(1)   (Show Source): You can put this solution on YOUR website!
3 divided by 2= 1.5.
It will take Hannah and Lindsay together 1 1/2 hours to clean the office.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
The rate of Hanna is  of the office area per hour.
In other words, Hanna is cleaning  of the office area per hour.

The rate of Lindsay is  of the office area per hour.
In other words, Lindsay is cleaning  of the office area per hour.

Working together, they are cleaning  +  =  +  =  of the office area per hour.

Hence, it will take  of hour (or 1 hour and 12 minutes) for Hanna and Lindsay to clean the office if they work together.

For more solved problems on joint work see the lesson Using fractions to solve word problems on joint work in this site.


Answer by cparks1000000(5)   (Show Source): You can put this solution on YOUR website!
Let be the amount of office space that Hanna can clean in 1 hour and be the amount of office space that Lindsay can clean in 1 hour. Let be the surface area of the room. Then and . Then let be the time it takes Hanna and Lindsay too clean the room together. Then .
Finally we solve for and in the equations not involving then plug into the third equation to get:

Then multiply through by to yield:

Thus the time it takes for them to clean the room together is 1.2 hours which is 1 hour and 12 minutes.
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