SOLUTION: It takes one painter 20 hours longer to pain a hoise than it does a more experienced painter. Together they paint the house in 24 hours. How long does it take for each painter to p

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Question 692040: It takes one painter 20 hours longer to pain a hoise than it does a more experienced painter. Together they paint the house in 24 hours. How long does it take for each painter to paint the house working alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hours for experienced painter
to paint house
+t+%2B+20+ = other painter's time in hours to paint house
Add their rates of painting to get rate working together
+1%2Ft+%2B+1%2F%28+t+%2B+20+%29+=+1%2F+24+
Multiply both sides by +24t%2A%28+t+%2B+20+%29+
+24%2A%28+t%2B20+%29+%2B+24t+=+t%2A%28+t%2B20+%29+
+24t+%2B+480+%2B+24t+=+t%5E2+%2B+20t+
+t%5E2+-+28t+-+480+=+0+
I'll complete the square
+t%5E2+-+28t+=+480++
+t%5E2+-+28t+%2B+%2828%2F2%29%5E2+=+480+%2B+%2828%2F2%29%5E2+
+t%5E2+-+28t+%2B+196+=+480+%2B+196+
+%28+t+-+14+%29%5E2+=+676+
+t+-+14+=+26+
+t+=+40+
+t+%2B+20+=+60+
It takes them 40 hrs for experienced painter
and 60 hrs for other painter
check:
+1%2Ft+%2B+1%2F%28+t+%2B+20+%29+=+1%2F+24+
+1%2F40%2B+1%2F60+=+1%2F+24+
Multiply both sides by 120
+3+%2B+2+=+5+
OK