SOLUTION: When working alone, Bob takes 3 hours longer then Janet to paint a certain size room. When working together, Bob and Janet can do the job in 2 hours. Calculate how long it takes

Algebra ->  Rate-of-work-word-problems -> SOLUTION: When working alone, Bob takes 3 hours longer then Janet to paint a certain size room. When working together, Bob and Janet can do the job in 2 hours. Calculate how long it takes       Log On


   

Question 734821: When working alone, Bob takes 3 hours longer then Janet to paint a certain size room. When working together, Bob and Janet can do the job in 2 hours. Calculate how long it takes each of them to individually paint the room
I'm just completely lost on how to set it up.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Janet's time in hours to paint room
+t+%2B+3+ = Bob's time in hours to paint room
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Janet's rate of working is ( 1 room painted ) / ( t hrs )
Bob's rate of working is ( 1 room painted ) / ( t + 3 hrs )
Their rate working together is ( 1 room painted ) / ( 2 hrs )
Add individual rates of working to get their
rate working together
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+1%2Ft+%2B+1%2F%28+t%2B3+%29+=+1%2F2+
Multiply both sides by +2t%2A%28+t%2B3+%29+
+2%2A%28+t%2B3+%29+%2B+2t+=+t%2A%28+t%2B3+%29+
+2t+%2B+6+%2B+2t+=+t%5E2+%2B+3t+
+t%5E2+-+t+-+6+=+0+
+%28+t-3+%29%2A%28+t%2B2+%29+=+0+
+t+=+3+ ( ignore the negative time )
+t+%2B+3+=+6+
Janet's time is 3 hrs to paint room
Bob's time is 6 hrs hours to paint room
check:
+1%2Ft+%2B+1%2F%28+t%2B3+%29+=+1%2F2+
+1%2F3+%2B+1%2F%28+3%2B3+%29+=+1%2F2+
+2%2F6+%2B+1%2F6+=+1%2F2+
+3%2F6+=+3%2F6+
OK