I'm trying to help my wife with a math problem and I couldn't figure out the solution. It been a long time since I've done this type a math and it's bothering me that I can't solve it. I don't have the question in front of me right now, but basically it goes like this: Someone wants to know how long it would take to fill up a tank a water. If you turn on the valve to fill the tank of water it takes 6 hours to fill an empty. If you turn on the valve to empty a tank, it take 10 hours to empty a full tank. How long would it take to fill up a tank of water if both valve to filled the tank and emptied the takes were both open. The answers says it takes 15hrs, but I want to know how they solve the problem. Know what I mean? So far all i can figure out is: let x represent how long it would take to fill the water tank when empty let y represent how long it would take to empty the water tank when full x + y = 16hrs - the time to both empty and filled the tank. I can't figure out the second equation, but I think it goes something like 1/6x - 1/10y = t am I even on the right track? BTW I haven't been in school for over ten years, so this isn't some kind of homework for me. So I don't have any teacher around to help me out, but some of you guy are pretty darn smart. Just like a teacher I know you can help me out. Any help would be appreciated. Thanks.

Every 1 hour you get 1/6 of the tank full, and 1/10 empties. That simplifies to a speed of 4/60ths an hour. Use that to get the answer. You were looking too hard.

Let the tank's size be T litres.

The rate of inflow is T/6 liters per hour. The rate of outflow is T/10 liters per hour.

So, with both taps on, the net rate of inflow is T/6 - T/10 = 10T/60 - 6T/60 = 4T/60 = T/15 liters per hour.

So, the tank will take 15 hours to fill.

Ahh. Thanks you guys.

I may have another question later for you to answer, but that was very helpful. It's been a long time since I've done anything like that I'm a little rusty.