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 1 pm and his mothers starts helping at 2, at what time will joey

Question 245005: It takes Joey 10 hours to clean his room, it takes his mother 5 hours to clean his room, if Joey starts cleaning at 1 pm and his mothers starts helping at 2, at what time will joeys room be clean...
Thank you.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes Joey and his mom to finish cleaning the room after his mom starts helping.
Joey cleans his room at the rate of 1/10 room per hour
His mother cleans his room at the rate of 1/5 room per hour
Together Joey and his mom cleans at the rate of 1/10+1/5=1/10 + 2/10=3/10 room per hour
In 1 hour, Joey cleans 1/10 of his room leaving 9/10 of the room yet to be cleaned. Now the question becomes: Working at the rate of 3/10 room per hour, how long will it take Joey and his mom to clean 9/10 of the room (finish cleaning)? So our equation to solve is:
(3/10)x=9/10 or
3x=9
x=3 hours-----amount of time it takes Joey and his mom to finish cleaning the room after his mom starts helping at 2 pm.
So 2pm + 3 hours=5:00pm---time that Joey's room will be clean.
CK
Joey cleans for 4 hrs at the rate of 1/10 room per hour---his effort gets 4/10 of the room clean
His mom cleans for 3 hours at the rate of 1/5 room per hour--her effort gets 3/5 or 6/10 of the room clean.
And---4/10+ 6/10=10/10 or 1 room!!!!!
Hope this helps---ptaylor

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