Name: Solving Free Fall Problem Using Quadratic Equation
Uploaded: 2019-07-19
Duration: 7 min 7 s
Description: In this video, we will learn how we can solve the problem of free fall effectively using the quadratic equation. Let's watch the video and learn.

Question

Two pipes running together can fill a cistern in

3 \frac{1}{13}

minutes. If one pipe takes

3

minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.

Accepted Answer

Let one pipe takes $x$ minutes to fill the cistern.

So, in $1$ minute, this pipe fills $\frac{1}{x}$ part of the cistern.

Second pipe takes $x + 3$ minutes to fill the cistern.

So, in $1$ minute, the pipe fills $\frac{1}{x + 3}$ part of the cistern.

So, in $1$ minute two pipes together will fill $\frac{1}{x} + \frac{1}{x + 3}$ part of the cistern.

So, two pipes together will fill up the cistern in $\frac{1}{\frac{1}{x} + \frac{1}{x + 3}}$ minutes.

Thus, by the given condition, we have,

$\frac{1}{\frac{1}{x} + \frac{1}{x + 3}} = 3 \frac{1}{13} = \frac{40}{13} \Rightarrow \frac{1}{\frac{x + 3 + x}{x (x + 3)}} = \frac{40}{13} \Rightarrow \frac{x^{2} + 3 x}{2 x + 3} = \frac{40}{13} \Rightarrow 13 x^{2} + 39 x = 80 x + 120 \Rightarrow 13 x^{2} - 41 x - 120 = 0$

$\Rightarrow 13 x^{2} - 65 x + 24 x - 120 = 0 \Rightarrow 13 x (x - 5) + 24 (x - 5) = 0 \Rightarrow (13 x + 24) (x - 5) = 0 \Rightarrow 13 x + 24 = 0 or x - 5 = 0 \Rightarrow x = - \frac{24}{13}, 5$

$x$ being time, cannot be negative. Thus, $x = 5$ minutes..

Therefore, one pipe fill up the cistern in $5$ minutes and the other pipe will fill up the cistern in $x + 3 = 5 + 3 = 8$ minutes.

Two pipes running together can fill a cistern in $3 \frac{1}{13}$ minutes. If one pipe takes $3$ minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

Two pipes running together can fill a cistern in 3113 minutes. If one pipe takes 3 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

Two pipes running together can fill a cistern in $3 \frac{1}{13}$ minutes. If one pipe takes $3$ minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.