SOLUTION: An experienced painter can paint a fence twice as fast as an inexperienced painter. Working together, they can paint the fence in 4 hours. How long would it take the experienced pa

Algebra ->  Rate-of-work-word-problems -> SOLUTION: An experienced painter can paint a fence twice as fast as an inexperienced painter. Working together, they can paint the fence in 4 hours. How long would it take the experienced pa      Log On


   

Question 512436: An experienced painter can paint a fence twice as fast as an inexperienced painter. Working together, they can paint the fence in 4 hours. How long would it take the experienced painter to paint it by himself?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
The rate of the 2 painters together is:
( 1 fence ) / ( 4 hrs )
Let +t+ = the time for the experienced painter
to paint 1 fence, so his rate is:
( 1 fence ) / ( t hrs )
The inexperienced painter will take twice as long:
( 1 fence ) / ( 2t ) hrs
-----------------
I can add their rates of painting to get the rate
when they work together
+1%2Ft+%2B+1%2F%282t%29+=+1%2F4+
Multiply both sides by +4t+
+4+%2B+2+=+t+
+t+=+6+
The experienced painter takes
6 hrs to paint the fence alone