Name: Introduction to Quadratic Equations
Uploaded: 2019-07-19
Duration: 44 min 45 s
Description: This video discusses the basic concepts of Quadratic Equations. After watching this video you will have a clear idea about how to solve and applications of Quadratic Equations.

Question

Two water pipes together can fill a tank in

1 \frac{7}{8} hours

. The tap with larger diameter takes

2 hours

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

Accepted Answer

Let the time taken by the smaller diameter tap to fill the tank be $x h r .$

Time taken by the larger diameter tap $= (x - 2) h r$ .

Volume of tank filled by smaller tap in $1$ hour $= \frac{1}{x}$

Volume of tank filled by larger tap in $1$ hour $= \frac{1}{x - 2}$

As per the question, the tank can be filled in $1 \frac{7}{8} = \frac{15}{8}$ hours by both the taps together.

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

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

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

$\Rightarrow 15 (2 x - 2) = 8 x^{2} - 16 x$

$\Rightarrow 30 x - 30 = 8 x^{2} - 16 x$

$\Rightarrow 8 x^{2} - 46 x + 30 = 0$

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

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

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

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

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

$i . e ., x = 5$ or $x = \frac{3}{4}$

Taking $x = \frac{3}{4}$

Time taken by smaller tap $= x = \frac{3}{4} hrs$

Time taken by larger tap $= x - 2$ $= \frac{3}{4} - 2 = \frac{3 - 8}{4} = - \frac{5}{4}$

Since time is negative, $x = - \frac{5}{4}$ is not the solution.

Thus, the time taken separately by the smaller diameter tap and the larger diameter tap will be $5$ hours and $(5 - 2) = 3$ hours respectively.

Two water pipes together can fill a tank in $1 \frac{7}{8} hours$ . The tap with larger diameter takes $2 hours$ less than the tap with smaller diameter 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 pipes together can fill a tank in 178 hours. The tap with larger diameter takes 2 hours less than the tap with smaller diameter 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 pipes together can fill a tank in $1 \frac{7}{8} hours$ . The tap with larger diameter takes $2 hours$ less than the tap with smaller diameter to fill the tank separately. Find the time in which each tap can fill the tank separately.