Two taps running together can fill a tank in 3$\frac{1}{13}$ hours, If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fil the tank ?

Given: Time taken to fill the tank together by the two taps=3$\frac{1}{13}$ hours.

To do: To find the time taken by each tap to fill the tank.

Solution:

Two taps when run together fill the tank in $3\frac{1}{13} \ hrs=\frac{40}{13} \ hours$

Let us say taps are A, B, And A fills the tank by itself in $x\ hrs$

B fills tank in $( x+3) \ hrs$

Portion of tank filled by A $( in\ 1\ hr) \ =\frac{1}{x}$

Portion of tank filled by B $( in\ 1\ hr) \ =\frac{1}{x+3}$

Portion of tank filled by A & B $( both\ in\ 1\ hr) \ =\frac{1}{x} +\frac{1}{x+3} =\frac{13}{40}$

$\frac{1}{x} +\frac{1}{x+3} =\frac{13}{40}$

$\Rightarrow \frac{x+3+x}{x( x+3)} =\frac{13}{40}$

$\Rightarrow \frac{2x+3}{x^{2} +3x} =\frac{13}{40}$

$\Rightarrow 40( 2x+3) =13\left( x^{2} +3x\right)$

$\Rightarrow 80x+120=13x^{2} +39x$

$\Rightarrow 13x^{2} -39x-80x-120=0$

$\Rightarrow 13x^{2} -41x-120=04$

on solving the equation we get,

$x=5\ hrs$.

Thus tap A will take 5 hours to fill the tank and tap B will take $5+3=8$ hours to fill the tank.
 

Tutorialspoint
Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

5K+ Views

Related Articles

Kickstart Your Career

Get certified by completing the course

Get Started
Advertisements