Question

A large tank initially contains 1 L of water. A tap is connected to the tank, which fills the tank at a rate of 3 L per minute. Determine the quantity of water in the tank as function of time and find the quantity water in the tank after 10 minutes of the tap opening, given that there is no over flowing or loss of water from the tank.

L

Answer 1

Let's express the quantity of water in the tank as a function of time.

Let time is denoted by $x$ minutes.
Rate of water filling $=3$ L per minute.

$\therefore$ Quantity of water filled in $x$ minutes $=3\times x=3x$ L

Initially, $1$ L of water was present.
$\therefore$ Quantity of water in the tank at $x$ minutes, $=3x+1$ L
$\Rightarrow f\left(x\right)=3x+1$

We need to find the quantity of water after $10$ minutes.
Substitute $10$ in the above equation.
$f\left(10\right)=3\left(10\right)+1=30+1=31$

$\therefore 31$ L of water will be present in the tank after $10$ minutes of the tap opening.