SOLUTION: Dana can paint a room alone in four hours. Cynthia can do the same job in three hours. How long will it take them to paint a similar room if they work together

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Dana can paint a room alone in four hours. Cynthia can do the same job in three hours. How long will it take them to paint a similar room if they work together       Log On


   



Question 729757: Dana can paint a room alone in four hours. Cynthia can do the same job in three hours. How long will it take them to paint a similar room if they work together

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
add their rates of working
Let +t+ = hrs to paint room with both working
( 1 room / 4 hrs ) + ( 1 room / 3 hrs ) = 1 room / t hrs
+1%2F4+%2B+1%2F3+=+1%2Ft+
Multiply both sides by +12t+
+3t+%2B+4t+=+12+
+7t+=+12+
+t+=+12%2F7+ hrs