question_answer

Two pipes running together can fill a tank in \[11\frac{1}{9}\] minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

Answer:

Let the time taken by the one tap to fill the tank be x minutes.

then, other pipe takes \[(x+5)\] minutes to fill the tank.

According to the question,

\[\frac{1}{x}+\frac{1}{x+5}=\frac{1}{100/9}\]

\[\frac{x+5+x}{x(x+5)}=\frac{9}{100}\]

\[100(5+2x)=9x(x+5)\]

\[500+200x=9{{x}^{2}}+45x\]

\[9{{x}^{2}}+45x-200x-500=0\]

\[9{{x}^{2}}-155x-500=0\]

\[9{{x}^{2}}-180x+25x-500=0\]

\[9x(x-20)+25(x-20)=0\]

\[(9x+25)(x-20)=0\]

\[x=20\] or \[-\frac{25}{9}\] (Neglect)

\[\therefore x=20\]

\[\therefore \] Time in which each pipe would fill the tank separately are 20 mins and 25 mins respectively.