SOLUTION: It takes one painter 20 hours longer to paint a house than it does a more experienced painter. Together they can paint a house in 24 hours. How long does it take each painter to pa

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes one painter 20 hours longer to paint a house than it does a more experienced painter. Together they can paint a house in 24 hours. How long does it take each painter to pa      Log On


   

Question 633181: It takes one painter 20 hours longer to paint a house than it does a more experienced painter. Together they can paint a house in 24 hours. How long does it take each painter to paint the house working alone?
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
24/(x+20)+24/x=1
x=40 and x+20=60
check
24/40+24/60=1
3/5+2/5=1
ok

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time it takes the more experienced painter
to paint the house
+t+%2B+20+ = time for less experienced painter
---------
Add their rates of painting to get rate working together
+1%2Ft+%2B+1%2F%28+t+%2B+20+%29+=+1%2F24+
Multiply both sides by +120t%2A%28+t+%2B+20+%29+
+120%2A%28+t+%2B+20+%29+%2B+120t++=+5t%2A%28+t+%2B+20+%29+
+120t+%2B+2400+%2B+120t+=+5t%5E2+%2B+100t+
+5t%5E2+-+140t+-+2400+=+0+
+t%5E2+-+28t+-+480+=+0+
+t%5E2+-++28t+=+480+
Complete the square
+t%5E2+-+28t+%2B+%2828%2F2%29%5E2+=+480+%2B+%2828%2F2%29%5E2+
+t%5E2+-+28t+%2B+196+=+676+
+%28+t+-+14+%29%5E2++=+26%5E2+
+t+-+14+=+26+
+t+=+40+
40 hrs = the time it takes the more experienced painter
to paint the house
60 hrs = time for less experienced painter