SOLUTION: please help me solve this problem Suppose one carpet layer can carpet an entire house in 4 hours more than the second guy. It takes the two carpet layers together three hours to

Algebra ->  Rate-of-work-word-problems -> SOLUTION: please help me solve this problem Suppose one carpet layer can carpet an entire house in 4 hours more than the second guy. It takes the two carpet layers together three hours to       Log On


   

Question 864356: please help me solve this problem
Suppose one carpet layer can carpet an entire house in 4 hours more than the second guy. It takes the two carpet layers together three hours to carpet the house. HOw long does it take each one alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of laying carpet to
get their rate working together:
2nd carpet layer:
( 1 house ) / ( t hrs )
1st carpet layer:
( 1 house ) / ( t + 4 )
working together:
( 1 house ) / ( 3 hrs )
-------------------------
+1%2Ft+%2B+1%2F%28+t%2B4+%29+=+1%2F3+
Multiply both sides by +t%2A%28+t%2B4+%29%2A3+
+3%2A%28+t+%2B+4+%29+%2B+3t+=+t%2A%28+t%2B4+%29+
+3t+%2B+12+%2B+3t+=+t%5E2+%2B+4t+
+t%5E2+-+2t+-+12+=+0+
completing the square:
+t%5E2+-+2t+=+12+
+t%5E2+-+2t+%2B+%28+-2%2F2+%29%5E2+=+12+%2B+%28+-2%2F2+%29%5E2+
+t%5E2+-+2t+%2B+1+=+12+%2B+1+
+%28+t+-+1+%29%5E2+=+13+
Take the square root of both sides
+t+-+1+=+sqrt%2813%29+
+t+=+sqrt%2813%29+%2B+1+
and
+t+%2B+4+=+sqrt%2813%29+%2B+1+%2B+4+
------------------------------------
These are the answers in hours. Here's the plot
of the equation +t%5E2+-+2t+-+12+=+0+
+graph%28+400%2C+400%2C+-10%2C+10%2C+-16%2C+10%2C+x%5E2+-+2x+-+12+%29+
Use the positive solution because you can't
have negative time