SOLUTION: Amy can mow the lawn by herself in 2 less hours than it takes Bob to mow the lawn by himself. When they work together, it takes them only 6 hours to mow the lawn. How long would

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Amy can mow the lawn by herself in 2 less hours than it takes Bob to mow the lawn by himself. When they work together, it takes them only 6 hours to mow the lawn. How long would       Log On


   

Question 739360: Amy can mow the lawn by herself in 2 less hours than it takes Bob to mow the lawn by himself. When they work together, it takes them only 6 hours to mow the lawn. How long would it take each of them to mow the lawn working alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let Bob's rate of mowing = ( 1 lawn mowed ) / ( t hrs )
Amy's rate is ( 1 lawn mowed ) / ( t - 2 hrs )
Add their rates of mowing to get their
rate working together, which is:
( 1 lawn mowed ) / ( 6 hrs )
-------------------------
+1%2Ft+%2B+1%2F%28+t+-+2+%29+=+1%2F6+
Multiply both sides by +t%2A%28+t-2+%29%2A6+
+6%2A%28+t-2+%29+%2B+6t+=+t%2A%28+t-2+%29+
+6t+-+12+%2B+6t+=+t%5E2+-+2t+
+t%5E2+-+14t+%2B+12+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-14+
+c+=+12+
+t+=+%28-%28-14%29+%2B-+sqrt%28+%28-14%29%5E2+-+4%2A1%2A12+%29%29+%2F+%282%2A1%29+
+t+=+%28+14+%2B-+sqrt%28+196+-+48+%29%29+%2F+2+
+t+=+%28+14+%2B-+sqrt%28+148+%29%29+%2F+2+
+t+=+%28+14+%2B-+sqrt%28+4%2A37+%29%29+%2F+2+
+t+=+7+%2B-+sqrt%28+37+%29+
+t+=+7+%2B+6.0828+
+t+=+13.0828+
+t+-2+=+11.0828+
+.0828%2A60+=+5+ ( approximately )
Bob, working alone mows the lawn in 13 hrs, 5 min
Amy, working alone mows the lawn in 11 hrs 5 min
----------------
check:
+1%2Ft+%2B+1%2F%28+t+-+2+%29+=+1%2F6+
+1%2F13.0828+%2B+1%2F11.0828+=+1%2F6+
+.07644+%2B+.09023+=+.16667+
+.16667+=+.16667+
OK