SOLUTION: Nicole can paint a room in six hours, Alexandra can paint a room in 5 hours, and Liana can paint a room in 4 hours. If all three work together, how long will it take them to paint

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Nicole can paint a room in six hours, Alexandra can paint a room in 5 hours, and Liana can paint a room in 4 hours. If all three work together, how long will it take them to paint       Log On


   



Question 535406: Nicole can paint a room in six hours, Alexandra can paint a room in 5 hours, and Liana can paint a room in 4 hours. If all three work together, how long will it take them to paint the room?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of painting
( 1 room / 6 hrs ) + ( 1 room / 5 hrs ) + ( 1 room / 4 hrs ) = 1 room / x hrs
+1%2F6+%2B+1%2F5+%2B+1%2F4+=+1%2Fx+
Multiply both sides by 60x
+10x+%2B+12x+%2B+15x+=+60+
+37x+=+60+
+x+=+60%2F37+
+x+=+1.622+ hrs
+.622%2A60+=+37.3+
It will take them 1 hr and 37 min
check:
+1%2F6+%2B+1%2F5+%2B+1%2F4+=+1%2Fx+
+.1666+%2B+.2+%2B+.25+=+.6166+
+.6166+=+.6166+
OK