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
Sister 1 6
Both together 1 x
Then we make the equation by
Ruth's rate + Sister's rate = Rate together
+ =
Multiply through by 6x
2x + x = 6
3x = 6
x = 2
Answer: 2 hours.
Edwin