SOLUTION: Jane needs 3 hours to clean the Smith house. Her younger sister, Alice, can clean the house in 5 hours. How long would the sisters, working together, need to clean the house?

Question 882913: Jane needs 3 hours to clean the Smith house. Her younger sister, Alice, can clean the house in 5 hours. How long would the sisters, working together, need to clean the house?
Answer by Leaf W.(135) (Show Source): You can put this solution on YOUR website!
Hi!
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If Jane can clean the house in 3 hours, she is able to clean 1/3 of the house in an hour. Likewise, if Alice cleans the house in 5 hours, she can clean 1/5 of the house in an hour. Let us call the number of hours they need to clean the house (working together) x. Then, is the fraction of the house Jane can clean in that amount of time, and is the fraction of the house Alice can clean in that amount of time.
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Thus, you can create the equation , since you want the amount of the house Jane cleans plus the amount of the house Alice cleans to equal one (indicating one complete house). Now simply solve for x to find the amount of hours this will take:

Multiply by the least common denominator, 15:
Add together like terms:
Divide both sides by 8:
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Thus, the sisters need 15/8 hours to clean the house.
I hope this helps! =)
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