SOLUTION: An inlet pipe can fill a tank in 10 minutes. A drain can empty the tank in 20 minutes. If the tank is empty, and both the pipe and drain are open, how long will it take before the

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: An inlet pipe can fill a tank in 10 minutes. A drain can empty the tank in 20 minutes. If the tank is empty, and both the pipe and drain are open, how long will it take before the       Log On


   

Question 904583: An inlet pipe can fill a tank in 10 minutes. A drain can empty the tank in 20 minutes. If the tank is empty, and both the pipe and drain are open, how long will it take before the tank overflows?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Rate of filling:
( 1 tank ) / ( 10 min )
Rate of emptying:
( 1 tank ) / ( 20 min )
--------------------
Add the rates:
( minus sign means pipe empties )
+1%2F10+-+1%2F20+=+1%2Ft+
Multiply both sides by +20t+
+2t+-+t+=+20+
+t+=+20+
After 20 min, the tank overflows
-----------------------------
check:
Let +x+ = volume of tank filled
( 1 = tank filled )
+1%2F10+-+1%2F20+=+x%2F20.1+
( +20.1+ min have passed )
---------------------------
+2%2F20+-+1%2F20+=+x%2F20.1+
+1%2F20+=+x%2F20.1+
+20.1+=+20x+
+x+=+1.005+
( tank starts to overflow )