Andrea can clean a house in 4 times as fast as Denise. When they work together,Andrea & Denise can clean a large house in 8 hours. How many hours would it take Denise to clean the house by herself?

Question

anonymous · Answer

@Loser66

hero · Answer

@Loujoelou, are you aware of equation:

$\dfrac{M \times N}{M + N} = t$

M = time it takes 1st person to do a job alone
N = time it takes 2nd person to do a job alone
t = time it takes both to complete the job together?

anonymous · Answer

no :) 
so if i used that equation would it be:
4x*x       4x^2
-----=  ------ ?
4x+x         5x

hero · Answer

Yes, now what are you going to set that equal to?

anonymous · Answer

4x^2             4x
----- = t    ---- = t  ?
5x                 5

anonymous · Answer

x= 5/4 ?

hero · Answer

How did you get that? Show the work you did to arrive at that result.

hero · Answer

You do realize a value for t is given, right?

anonymous · Answer

sure ok so i cancelled an x on the top & bottom of: (4x^2)/(5x) & omg i forgot about the 8 hours!

anonymous · Answer

(4x/5)= 8 so 8*(5/4)=10! So the answer is 10 right?

hero · Answer

Congrats.

anonymous · Answer

Thanks for guiding me through the problem :)

hero · Answer

Nice job solving.