SOLUTION: Working together, Sarah and Heidi can clean the garage in 6 hours. If they work alone, it takes Heidi 9 hours longer than it takes Sarah. How long would it take Heidi to clean the

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Working together, Sarah and Heidi can clean the garage in 6 hours. If they work alone, it takes Heidi 9 hours longer than it takes Sarah. How long would it take Heidi to clean the       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 990269: Working together, Sarah and Heidi can clean the garage in 6 hours. If they work alone, it takes Heidi 9 hours longer than it takes Sarah. How long would it take Heidi to clean the garage alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of cleaning to get rate
working together
[ 1 garage cleaned ] / [ t hrs ] = Sarah's rate
[ 1 garage cleaned ] / [ t + 9 hrs ] = Heidi's rate
[ 1 garage cleaned ] / [ 6 hrs ] = their rate working together
-------------------------
+1%2Ft+%2B+1%2F%28+t%2B9+%29+=+1%2F6+
Multiply both sides by +6t%2A%28+t%2B9%29+
+6%2A%28+t+%2B+9+%29+%2B+6t+=+t%2A%28+t%2B+9+%29+
+6t+%2B+54+%2B+6t+=+t%5E2+%2B+9t+
+12t+%2B+54+=+t%5E2+%2B+9t+
+t%5E2+-+3t+-+54+=+0+
I notice that +6%2A9+=+54+
and +6+-+9+=+-3+, so
+%28+t+-+9+%29%2A%28+t+%2B+6+%29+=+0+
+t+=+9+ ( can't have +t+=+-6+, time can't be negative )
and
+t+%2B+9+=+18+
It will take Heidi 18 hrs to clean garage working alone
-----------------
check:
+1%2Ft+%2B+1%2F%28+t%2B9+%29+=+1%2F6+
+1%2F9+%2B+1%2F18+=+1%2F6+
+2%2F18+%2B+1%2F18+=+3%2F18+
+3%2F18+=+3%2F18+
OK