SOLUTION: Zeno takes 3hrs longer to piant a floor than it takes lia. When they work together, it takes them 2hrs. how long would each to get the job done?

Algebra ->  Rational-functions -> SOLUTION: Zeno takes 3hrs longer to piant a floor than it takes lia. When they work together, it takes them 2hrs. how long would each to get the job done?      Log On


   

Question 661572: Zeno takes 3hrs longer to piant a floor than it takes lia. When they work together, it takes them 2hrs. how long would each to get the job done?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time in hrs it
takes Lia to paint the floor
+t+%2B+3+ = time it takes Zeno
------------------
Add their rates of working to get their
rate working together
( 1 floor painted / Zeno's time ) + ( 1 floor painted ) / ( Lia's time )
= ( 1 floor painted ) / ( time for both painting together )
+1%2F%28t%2B3%29+%2B+1%2Ft+=+1%2F2+
Multiply both sides by +2%2At%2A%28+t+%2B+3+%29+
+2t+%2B+2%2A%28+t+%2B+3+%29+=+t%2A%28+t+%2B+3+%29+
+2t+%2B+2t+%2B+6+=+t%5E2+%2B+3t+
+t%5E2+-+t+-+6+=+0+
I can see that this is
+%28+t+-+3+%29%2A%28+t+%2B+2+%29+=+0+
+t+=+3+
( can't be +t+=+-2+ because you can't have negative time )
and
+t+%2B+3+=+6+
Lia takes 3 hrs to paint the floor
Zeno takes 6 hrs to paint the floor
check answer:
+1%2F%28t%2B3%29+%2B+1%2Ft+=+1%2F2+
+1%2F%283%2B3%29+%2B+1%2F3+=+1%2F2+
+1%2F6+%2B+2%2F6+=+3%2F6+
+3%2F6+=+3%2F6+
OK