SOLUTION: ruth can clean the room in 3 hours her younger sister can do the job in 6 hours how long if it take together?

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Question 520029: ruth can clean the room in 3 hours her younger sister can do the job in 6 hours how long if it take together?

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
ruth can clean the room in 3 hours her younger sister can do the job in 6 hours how long if it take together?
Without using algebra:
Ruth's rate is 1 room per 3 hours or 1/3 of a room per hour.
Her sister's rate is one room per 6 hours or 1/6 of a room per hour

Their combined rate is 1/3 + 1/6 or 1/2, that's half a room per hour,
so together they can clean a whole room in 2 hours.
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Using algebra:

Make this chart:
                    Number of
                  Rooms cleaned       Hours        Rate in rooms/hour
Ruth                   

Sister                

Both together          

Let x = the time in hours for both together to clean 1 room, so fill in
1 for the number of rooms cleaned and x for the time for both together.

                    Number of
                  Rooms cleaned       Hours        Rate in rooms/hour
Ruth                  

Sister                  

Both together           1               x

We are told that Ruth can clean 1 room in 3 hours, so we put 1 for
her number of hours and 3 for the hours.

                    Number of
                  Rooms cleaned       Hours        Rate in rooms/hour
Ruth                    1               3

Sister                  

Both together           1               x

We are told that her sister can clean 1 room in 6 hours, so we put 1 for
her number of hours and 6 for the hours.

                    Number of
                  Rooms cleaned       Hours        Rate in rooms/hour
Ruth                    1               3

Sister                  1               6

Both together           1               x

Next er fill in the three rates in rooms/hour by dividing the number
of rooms cleaned by the hours:

                    Number of
                  Rooms cleaned       Hours        Rate in rooms/hour
Ruth                    1               3               1%2F3
Sister                  1               6               1%2F6 
Both together           1               x               1%2Fx

Then we make the equation by

        Ruth's rate  +  Sister's rate  =  Rate together

                                1%2F3 + 1%2F6 = 1%2Fx

Multiply through by 6x
                                2x + x = 6    
                                    3x = 6
                                     x = 2

Answer: 2 hours.

Edwin