Question 882913
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, {{{(1/3)x}}} is the fraction of the house Jane can clean in that amount of time, and {{{(1/5)x}}} is the fraction of the house Alice can clean in that amount of time.
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Thus, you can create the equation {{{(1/5)x + (1/3)x = 1}}}, 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:
{{{x/5 + x/3 = 1}}}
Multiply by the least common denominator, 15: {{{3x + 5x = 15}}}
Add together like terms: {{{8x = 15}}}
Divide both sides by 8: {{{x = 15/8}}}
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Thus, the sisters need 15/8 hours to clean the house. 
I hope this helps! =)