SOLUTION: To paint a room, it takes Mike 75 minutes, Joan 60 minutes, and Kyle 80 minutes when each person works alone. If all three work together, how long will the painting take?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: To paint a room, it takes Mike 75 minutes, Joan 60 minutes, and Kyle 80 minutes when each person works alone. If all three work together, how long will the painting take?      Log On


   

Question 899314: To paint a room, it takes Mike 75 minutes, Joan 60 minutes, and Kyle 80 minutes when each person works alone. If all three work together, how long will the painting take?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of painting:
Mike's rate:
( 1 room ) / ( 75 min )
Joan's rate:
( 1 room ) / ( 60 min )
Kyle's rate:
( 1 room ) / ( 80 min )
----------------------
Let +t+ = time in minutes with
all 3 painting:
+1%2F75+%2B1%2F60+%2B+1%2F80+=+1%2Ft+
Multiply both sides by +5+
+1%2F15+%2B+1%2F12+%2B+1%2F16+=+5%2Ft+
Multiply both sides by +240t+
+16t+%2B+20t+%2B+15t+=+1200+
+51t+=+1200+
+t+=+23.53+
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with all 3 painting it will take 23.53 min
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check:
+1%2F75+%2B1%2F60+%2B+1%2F80+=+1%2Ft+
+1%2F75+%2B1%2F60+%2B+1%2F80+=+1%2F23.53+
+.01333+%2B+.01666+%2B+.0125+=+.0425+
+.04249+=+.0425+
close enough