Name: Formation of Quadratic Equation
Uploaded: 2019-07-19
Duration: 2 min 49 s
Description: We learned how to solve a quadratic equation using different methods. But do you know how to form a quadratic equation with the given roots? Let’s learn in detail here.

Question

Two water taps together can fill a tank in

1 \frac{7}{8}

hours. The tap with longer diameter takes

2

hours less than the tap with smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.

Accepted Answer

Let the smaller diameter tap fills the tank alone in $x$ hours then the larger diameter tap fills the tank alone in $(x - 2)$ hours.
In $1$ hour, the smaller diameter tap can fill $\frac{1}{x}$ part of the tank.
In $1$ hour, the larger diameter tap can fill $\frac{1}{(x - 2)}$ part of the tank.
Two water taps together can fill a tank in $\frac{15}{8}$ hours.
But in $1$ hour the taps fill $\frac{8}{15}$ part of the tank.

Acc. to question:

$\frac{1}{x} + \frac{1}{(x - 2)} = \frac{8}{15}$

$\Rightarrow \frac{x - 2 + x}{x (x - 2)} = \frac{8}{15}$

$\Rightarrow \frac{2 (x - 1)}{x^{2} - 2 x} = \frac{8}{15}$

$\Rightarrow 4 x^{2} - 8 x = 15 x - 15$

$\Rightarrow 4 x^{2} - 23 x + 15 = 0$

$\Rightarrow 4 x^{2} - 20 x - 3 x + 15 = 0$

$\Rightarrow 4 x (x - 5) - 3 (x - 5) = 0$

$\Rightarrow (4 x - 3) (x - 5) = 0$

$\Rightarrow x = 5$ or $x = \frac{3}{4}$

If $x = \frac{3}{4}$ then $x - 2 = - \frac{5}{4}$ which is not possible since time cannot be negative.

Therefore, $x = 5$ and $x - 2 = 3$ .

Hence, larger diameter tap can fill the tank in $5$ hours and smaller diameter tap can fill the tank in $3$ hours.

Two water taps together can fill a tank in $1 \frac{7}{8}$ hours. The tap with longer diameter takes $2$ hours less than the tap with smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

Two water taps together can fill a tank in 178 hours. The tap with longer diameter takes 2 hours less than the tap with smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

Two water taps together can fill a tank in $1 \frac{7}{8}$ hours. The tap with longer diameter takes $2$ hours less than the tap with smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.