SOLUTION: Eric can paint a room in 9 hours. Working together, Eric and Matt can paint the room in 4 hours. How long will it take Matt to paint the room by himself?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Eric can paint a room in 9 hours. Working together, Eric and Matt can paint the room in 4 hours. How long will it take Matt to paint the room by himself?      Log On


   

Question 871396: Eric can paint a room in 9 hours. Working together, Eric and Matt can paint the room in 4 hours. How long will it take Matt to paint the room by himself?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Their combined rate is the sum of their individual rates.

1%2F9%2Br=1%2F4, using r as Matt's rate. The rate unit is rooms per hour. Solve for r, and find the reciprocal. THAT is how long the time for Matt to paint the room himself.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Eric's rate of painting is
( 1 room painted ) / ( 9 hrs )
Together, their rate is:
( 1 room painted ) / ( 4 hrs )
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Let Matt's rate of painting =
( 1 room painted ) / ( t hrs )
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Add their rates to get their rate
working together
+1%2F9+%2B+1%2Ft+=+1%2F4+
Multiply both sides by +36t+
+4t+%2B+36+=+9t+
+5t+=+36+
+t+=+7.2+
Note that +.2+ hrs = +.2%2A60+=+12+ min
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Matt can paint the room by himself in 7 hrs 12 min