SOLUTION: Carl can paint a room 3 hours faster than Jennifer can. If they work together, they can complete the job in 2 hours. Using complete sentences, explain each step in figuring out how

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Question 891733: Carl can paint a room 3 hours faster than Jennifer can. If they work together, they can complete the job in 2 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jennifer to complete this job on her own.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) Carl's rate of painting added to Jennifer's rate
of painting equals their rate of painting when
they work together
(2) Carl's rate is known, and so is their rate when
working together, so Jennifer's rate can be found
(3) Let Jennifer's rate = ( 1 room painted ) / ( t hours )
(4) Carl's rate = ( 1 room painted ) / ( ( t - 3 ) hours )
(5) Working together, their rate = ( 1 room painted ) / ( 2 hours )
(6) The equation is:
+1+%2F+%28+t-3+%29+%2B+1%2Ft+=+1%2F2+
(7) Multiply both sides by +2t%2A%28+t-3+%29+
(8) +2t+%2B+2%2A%28+t-3+%29+=+t%2A%28+t-3+%29+
(9) +2t+%2B+2t+-+6+=+t%5E2+-+3t+
+t%5E2+-+7t+%2B+6+=+0+
(10 ) Use the quadratic formula to solve for +t+, Jennifer's time