word problem

For me, it is easier to think about this problem if I make up the size of the tank. Let's say the tank holds 40 liters. As stated in the problem, it will take 40 minutes to fill the take and 60 minutes to drain it. Making the tank hold 40 liters doesn't change the problem at all.

However, if we know how large the tank is, we can figure out the rate that the substance (let's assume it is water) flows in and out of the tank. The calculation for a rate is easy - it is just the number of liters divided by the number of minutes. We care about two different rates - the fill rate and the drain rate.

Fill rate: we know it takes 40 minutes to fill up 40 liters. So, 40 liters divided by 40 minutes = 1 liter per minute. Water flows into the tank at 1 liter every minute.

Drain rate: It takes 60 minutes to drain out 40 liters. So, 40 liters / 60 minutes = 2/3 liter per minute. Water flows out of the tank at 2/3 liter per minute.

With these two rates, solving the problem is much easier. We decided to make the tank hold 40 liters, so we want to solve for the number of minutes it takes to fill up the tank to 40 liters if the water is both filling up the tank and draining out of the tank. Thus we want the following equation: Liters in tank = (fill rate - drain rate) * number of minutes to fill.

40 liters = (1 liter per minute - 2/3 liter per minute) * Y minutes.

40 = (1 - 2/3) * Y

I'll leave solving for Y to you.

Help needed here please

A tank initially contains 7 gallons of water. A faucet is opened and water begins pouring into the tank at a rate of 1.5 gallons per minute untill the tank is full. Which of the following represents the volume v of water , in gallons, in the tank as a function of time t , in minutes, that has elapsed since the faucet was opened?
A) V(t) = 1.5+ t
B) V(t) = 8.5+ t
C) V(t) = 1.5t
D) V(t) = 1.5t -7
E) V(t) = 1.5t +7
Thanks in advance

Shereen, would you be more specific about what you are having trouble understanding?

Basically, you want to find the number of gallons V after a certain number of minutes, t. The final number of gallons in the tank will be equal to the initial amount in the tank plus however much pours into the tank. The amount that pours into the tank will equal the rate that it pours into the tank multiplied by how long the faucet is open. 

It is perhaps easier to understand by including the units for each term: final (gallons) = initial (gallons) + rate (gallons per minute) * time (minutes). 

That's what I know well but some math teachers insisted that he needed only the volume that increased after opening the faucet not the total volume including the initial
Which I totally disagree with
So I needed a second opinion frof khan academy to confirm whether it is C or E

Well, you need to include initial if you want the total volume in the tank and you don't need the initial volume if you just want to know how much was added to the tank. The disagreement between you and your teacher should be resolvable based on what the specific question asked for - as it is stated above, it seems to me that the question is looking for the total amount in the tank, not just the amount added. Explaining your reasoning on the question should be sufficient, rather than an appeal to the internet. I'm not part a member of Khan Academy's staff, just someone who likes helping out.