SOLUTION: Two companies working together can clear a parcel of land in 13 hours. Working alone, it would take company A 10 hours longer to clear the land than it would Company B. How long wo

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Two companies working together can clear a parcel of land in 13 hours. Working alone, it would take company A 10 hours longer to clear the land than it would Company B. How long wo      Log On


   

Question 747253: Two companies working together can clear a parcel of land in 13 hours. Working alone, it would take company A 10 hours longer to clear the land than it would Company B. How long would it take company B to clear the parcel of land alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get their rate working together
Let +t+ = B's time in hours to clear the parcel of land
given:
B's rate:
( 1 parcel cleared ) / ( t hrs )
A's rate:
( 1 parcel cleared ) / ( t + 10 hrs )
Their rate working together:
( 1 parcel cleared / t hrs ) + ( 1 parcel cleared / t + 10 hrs ) = ( 1 parcel cleared / 13 hrs )
----------------------
+1%2Ft+%2B+1%2F%28+t+%2B+10+%29+=+1%2F13+
Multiply both sides by +t%2A%28+t%2B10+%29%2A13+
+13%2A%28+t+%2B+10+%29+%2B+13t+=+t%2A%28+t+%2B+10+%29+
+13t+%2B+130+%2B+13t+=+t%5E2+%2B+10t+
+t%5E2+-16t+-+130+=+0+
Complete the square
+t%5E2+-+16t+=+130+
+t%5E2+-+16t+%2B+%28-16%2F2%29%5E2+=+130+%2B+%28-16%2F2%29%5E2+
+t%5E2+-16t+%2B+64+=+130+%2B+64+
+%28+t+-+8+%29%5E2+=+194+
Take square root of both sides
+t+-+8+=+13.928+
+t+=+21.928+
+.928%2A60+=+55.7+
Working alone, B takes 21 hrs 56 min
check:
+1%2Ft+%2B+1%2F%28+t+%2B+10+%29+=+1%2F13+
+1%2F21.928+%2B+1%2F%28+21.928+%2B+10+%29+=+1%2F13+
+.0456+%2B+.0313+=+.0769+
+.0769+=+.0769+
OK