SOLUTION: It takes Joey 10 hours to clean his room. It takes his mother 5 hours to clean his room. If Joey starts cleaning at 1pm and his mother starts helping at 2pm, at what time will joey

Question 241563: It takes Joey 10 hours to clean his room. It takes his mother 5 hours to clean his room. If Joey starts cleaning at 1pm and his mother starts helping at 2pm, at what time will joeys room be clean?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
joey takes 10 hours to clean his room which means that he can clean 1/10 of the room in 1 hour.
joey's mom takes 5 hours to clean his room which means that she can clean 1/5 of the room in 1 hour.
J = rate that joey takes per hour to clean his room = 1/10
M = rate that joey's mom takes per hour to clean his room = 1/5
C = their combined rate = (1/10 + 1/5) = 3/10 of the room in one hour.
The unit to be cleaned is a room.
The number of units to be cleaned is 1.

joey cleans for 1 hours so he has cleaned 1/10 * 1 = 1/10 of the room.

this leaves 9/10 of the room to be cleaned.

joey and his mother working together can clean 3/10 of the room in 1 hour.

since 9/10 of the room remain to be cleaned, this means that they will have the rest of the room cleaned in 3 hours.

1 * (1/10) + 3 * (3/10) = 1/10 + 9/10 = 1

basic formula used is R*T = U

this means that the Rate * Time = the number of units cleaned.

Rate is given in number of units per hour.
Time is given in number of hours.
Units is given in number of rooms to be cleaned.

the application of this formula is what solves the problem.

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