SOLUTION: It takes Earl 2 hours to paint a fence. It would take 3 hours for Ted to paint a same fence. If Earl and Ted work together to paint half the fence, then Earl leaves and Ted paints

Algebra ->  Proportions  -> Lessons -> SOLUTION: It takes Earl 2 hours to paint a fence. It would take 3 hours for Ted to paint a same fence. If Earl and Ted work together to paint half the fence, then Earl leaves and Ted paints       Log On


   

Question 1136307: It takes Earl 2 hours to paint a fence. It would take 3 hours for Ted to paint a same fence. If Earl and Ted work together to paint half the fence, then Earl leaves and Ted paints the rest of the fence by himself, how long would it take in total for the fence to be painted>
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get rate working together:
Let +t+ = time in hrs to paint 1/2 the fence
+1%2F2+%2B+1%2F3+=+%28%281%2F2%29%29%2Ft+
Multiply both sides by +6t+
+3t+%2B+2t+=+3+
+5t+=+3+
+t+=+3%2F5+
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Then Ted paints 1/2 the fence alone.
Let +t%5B1%5D+ = his time to paint 1/2 of the fence
+1%2F3+=+%28%281%2F2%29%29%2Ft%5B1%5D+
Multiply both sides by +3t%5B1%5D+
+t%5B1%5D+=+3%2F2+
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+t+%2B+t%5B1%5D+=+3%2F5+%2B+3%2F2+
+t+%2B+t%5B1%5D+=+6%2F10+%2B+15%2F10+
+t+%2B+t%5B1%5D+=+2.1+ hrs
convert to hrs + min
+.1%2A60+=+6+ min
Total time to paint the fence is 2 hrs 6 min
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