SOLUTION: if a person takes 10 hours to clean his room. It takes his mother 5 hours to clean his room. If that person starts cleaning a 1pm and his mother starts helping at 2pm, at what ti

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: if a person takes 10 hours to clean his room. It takes his mother 5 hours to clean his room. If that person starts cleaning a 1pm and his mother starts helping at 2pm, at what ti      Log On

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Question 548143: if a person takes 10 hours to clean his room. It takes his mother 5 hours to clean his room. If that person starts cleaning a 1pm and his mother starts helping at 2pm, at what time will it take the room to be clean?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First find the fraction of the room that
person cleans from 1 PM to 2 PM
Person's rate = ( 1 room ) / ( 10 hrs )
+%281%2F10%29%2A1+=+1%2F10+
Person cleans 1/10 of the room in 1 hr
There is 9/10 of the room left to clean
-------------------------------
Add their rates.
Let t = time for both to finish room
With person and Mother both cleaning:
+%28+1%2F10+%29+%2B+%28+1%2F5+%29+=+%289%2F10%29+%2F+t+
Multiply both sides by 10
+1+%2B+2+=+9%2Ft+
+t+=+9%2F3+
+t+=+3+ hrs
The room will be clean in +1+%2B+3+=+4+ hrs
4 hrs from 1 pm is 5 pm