SOLUTION: Together, Fay and Rob can paint a house in 3 days. It will take Rob 3 times as long as it will take Fay to do it alone. How long will take each of them to do it alone?

Algebra ->  Rational-functions -> SOLUTION: Together, Fay and Rob can paint a house in 3 days. It will take Rob 3 times as long as it will take Fay to do it alone. How long will take each of them to do it alone?      Log On


   

Question 1044282: Together, Fay and Rob can paint a house in 3 days. It will take Rob 3 times as long as it will take Fay to do it alone. How long will take each of them to do it alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Fay and Rob's rate working together is:
[ 1 house painted ] / [ 3 days ] = +1%2F3+
-----------------------------------
Let +t+ = Fay's time working alone
Fay's rate working alone is:
[ 1 house painted ] / [ t days ] = +1%2Ft+
-----------------------------------
Let +3t+ = Rob's time working alone
Rob's rate working alone is:
[ 1 house painted ] / [ 3t days ] = +1%2F%283t%29+
------------------------------------
Add their rates of painting to get their rate working together
+1%2Ft+%2B+1%2F%283t%29+=+1%2F3+
Multiply both sides by +3t+
+3+%2B+1+=+t+
+t+=+4+ days
and
+3t+=+12+ days
------------------
Fay can paint 1 house in 4 days
Rob can paiont 1 house in 12 days
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check:
+1%2Ft+%2B+1%2F%283t%29+=+1%2F3+
+1%2F4+%2B+1%2F12+=+1%2F3+
+3%2F12+%2B+1%2F12+=+4%2F12+
+4%2F12+=+4%2F12+
OK