SOLUTION: A tank can be filled in 2 hours. The same tank can be emptied in 6 hours. If the faucet is turned on and the drain is left open, when will the tank overflow?

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Question 713986: A tank can be filled in 2 hours. The same tank can be emptied in 6 hours. If the faucet is turned on and the drain is left open, when will the tank overflow?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rate of filling is ( 1 tank ) / ( 2 hrs )
The rate of draining is ( -1 tank ) / ( 6 hrs )
Let +t+ = time in hrs when tank starts to overflow
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I'm assuming that the tank starts out empty
Add the rates to get the total rate
Draining is a negative rate
+1%2F2+-+1%2F6+=+1%2Ft+
Multiply both sides by +6t+
+3t+-+t+=+6+
+2t+=+6+
+t+=+3+
The tank starts to overflow in 3 hrs