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. From the expression of the quantity of water in the tank as function of time, find after how many minutes of opening the tap, the quantity water in the tank is 14.5 L. It is known that there is no over flowing or loss of water from the tank.

minutes

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 time $x$ for the quantity of water $f\left(x\right)=14.5$ L.
Substitute $f\left(x\right)$ in the above equation.
$14.5=3x+1$
$\Rightarrow 3x=14.5-1=13.5$
$\Rightarrow x=\frac{13.5}{3}=4.5$

$\therefore 14.5$ L of water will be present in the tank after $4.5$ minutes of the tap opening.