SOLUTION: A water tank can be filled with a large inlet pipe and a small inlet pipe in three hours. The large inlet pipe alone can fll the tank in 2 hours less than the small inlet pipe alon

Algebra ->  Equations -> SOLUTION: A water tank can be filled with a large inlet pipe and a small inlet pipe in three hours. The large inlet pipe alone can fll the tank in 2 hours less than the small inlet pipe alon      Log On


   

Question 1121173: A water tank can be filled with a large inlet pipe and a small inlet pipe in three hours. The large inlet pipe alone can fll the tank in 2 hours less than the small inlet pipe alone. Find the time the tank can be filled by each pipe alone.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+1%2Ft+%2B+1%2F+%28+t-2+%29+=+1%2F3+
( adding the rates to get a rate working together )
Multiply both sides by +t%2A%28+t-2+%29%2A3+
+3%2A%28+t-2+%29+%2B+3t+=+t%2A%28+t-2+%29+
+3t+-+6+%2B+3t+=+t%5E2+-+2t+
+t%5E2+-+8t+%2B+6+=+0+
Complete the square
+t%5E2+-+8t+%2B+16+=+-6+%2B+16+
+%28+t+-+4+%29%5E2+=+10+
+t+-+4+=+sqrt%28+10+%29+
+t+=+4+%2B+3.1623+
+t+=+7.1623+
And
+t+-+2+=+5.1623+
Large pipe fills tank in 5.1623 hrs
Small pipe fills tank in 7.1623 hrs