SOLUTION: If Sam can paint a room in 4 hours and Gene can paint the same room in 6 hours but Timmy can paint the same room in 2 hours, how fast can they all paint the room together? I got t

Algebra ->  Rational-functions -> SOLUTION: If Sam can paint a room in 4 hours and Gene can paint the same room in 6 hours but Timmy can paint the same room in 2 hours, how fast can they all paint the room together? I got t      Log On


   

Question 834340: If Sam can paint a room in 4 hours and Gene can paint the same room in 6 hours but Timmy can paint the same room in 2 hours, how fast can they all paint the room together?
I got the answer: approximately 1.091 hours.
Is this correct? Thanks!
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
you know it has to be less than 2 because the fastest guy Tim can do it in 2
and Sam is half as fast
1.0909 or exactly 12/11

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hours
for all 3 to paint the room
-------------
Add their rates of painting:
+1%2F4+%2B+1%2F6+%2B+1%2F2+=+1%2Ft+
Multiply both sides by +12t+
+3t+%2B+2t+%2B+6t+=+12+
+11t+=+12+
+t+=+12%2F11+ hr
+t+=+1+%2B+1%2F11+ hrs
+1+ hr + +60%2F11+ min
+60%2F11+=+5.455+
+.455%2A60+=+27+
1 hr 5 min 27 sec
You got the same answer!