Help with an algebra word problem?

Let cindy clean the house in x hours and cara in y hours. So in 1 hour cindy cleans 1/x part of the house and cara cleans 1/y part of the house. Together in an hour they can clean 1/x + 1/y of the house. But together in an hour they clean 1/3rd of the house. So :

1/x + 1/y = 1/3

=> 1/x + 1/3x = 1/3 (Since cara takes 3 times longer than cindy hence y = 3x)

=> 4/3x = 1/3 => x = 4.

So cindy takes 4 hours to clean the house alone.

@CJ, Em and Shayla : If both can clean the house in 3 hours how can cindy alone do it in less than 3 hours ? She has to take more time. Common sense ?

Let Cindy take x hours to clean the house alone.

Then Cara takes 3x hours to clean the house alone.

In 1 hour Cindy does 1/ x of the house

In 1 hour Cara does 1/3x of the house

Together in 1 hour they do (1/ x + 1/ 3x ) of the house

i.e 4/ 3x of the house

4/3x = 1/3

3x = 12

x = 4

ANSWER Cindy = 4 hours Cara 12 hours

CHECK

1/4 +1/12 = 4/12 = 1/3

Together = 3 hours

Let Cindy's rate of cleaning be Y houses/hour

Let Cara's be A houses/hour

Cindy's rate = 3A

They together clean 1 house in 3 hours so

3A + 3*3A = 1

12A = 1

A = 1/12

Cindy's rate = 3A = 3/12 = 1/4 house/hours

So 1 house in 4 hours.

I did it by using algebra.

Let cindy = a cara=b

a+b = 3 (cindy and cara can clean the house together in 3 hours).

3b = a (cara takes 3 times longer than cindy)

now substiute the second equation into the first.

3b + b = 3

4b=3

b=3/4

So it takes cara 3/4 hours, which is 45 min to clean the house.

Now to find out how much time it takes for cindy put into original equation

a +b =3

a + 3/4 = 3

a= 2 1/4 (2hours and 15 min)

to check 3/4 x 3 = 2 1/4 hours

It takes 2 hours and fifteen minutes for cindy to clean the house by herself.

Put it in equations....... cindy= x and cara= y

3=x+y

Y=3x

Now just substitute.... hopefully you get it from here..