SOLUTION: it takes bob 10 hours to clean his room. It takes his mom 5 hours to clean his room. If bob starts cleaning at 1 pm and his mother starts helping at 2pm at what time will bob's roo

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Question 908325: it takes bob 10 hours to clean his room. It takes his mom 5 hours to clean his room. If bob starts cleaning at 1 pm and his mother starts helping at 2pm at what time will bob's room be clean?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
From 1 PM to 2 PM is 1 hr
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Bob's rate of cleaning is:
( 1 room ) / ( 10 hrs ) = +1%2F10+
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The fraction of the room cleaned by
Bob in +1+ hr is:
+1%2A%28+1%2F10+%29+=+1%2F10+ of the room
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That means there is +9%2F10+ of the
room left to clean
-----------------
Add Bob's rate and his Mom's rate to
get their rate working together:
Let +t+ = time in hrs for them to
finish working together
+1%2F10+%2B+1%2F5+=+%28%28+9%2F10%29%29+%2F+t+
Multiply both sides by +10t+
+t+%2B+2t+=+9+
+3t+=+9+
+t+=+3+
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3 hrs after 2 PM is 5 PM
They will finish cleaning the room at 5 PM