SOLUTION: A water tank can be filled in 7 minutes and emptied in 10 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

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Question 713473: A water tank can be filled in 7 minutes and emptied in 10 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The filling rate is one tank per 7 minutes or %281_tank%29%2F%287_minutes%29 or 1%2F7tank%2Fminute.

The emptying rate is NEGATIVE one tank per 10 minutes or -%281_tank%29%2F%2810_minutes%29 or -1%2F10tank%2Fminute.

So the filling rate when both are open is 1%2F7+-+1%2F10 = 10%2F70-+7%2F70 = 3%2F70%28tank%29%2F%28minutes%29 = %283_tanks%29%2F%2870_minutes%29

Set up a proportion

3 tanks is to 70 minutes as 1 tank is to X minutes

%283_tanks%29%2F%2870_minutes%29%22%22=%22%22%281_tank%29%2F%28X_minutes%29

Cross multiply and solve for X.

You'll get that it would take 70%2F3 or 23%261%2F3 minutes 20 seconds. 

Edwin