Question

Two pipes take $x$ minutes and $(x+3)$ minutes respectively to fill a cistern. If together they fill the cistern in $3\frac{1}{13}$ minutes, find the value of $x$.

Answer 1

Tank filled by pipe 1 in one minute = $\frac{1}{x}$
Tank filled by pipe 2 in one minute = $\frac{1}{x+3}$
Tank filled by both pipes in one minute = $\frac{13}{40}$
hence, $\frac{1}{x}+\frac{1}{x+3}=\frac{13}{40}$
$40(x+3+x)=13(x^2+3x)$
$80x+120=13x^2+39x$
$13x^2-41x-120=0$
$x=\frac{41\pm 89}{26}$
$x=\frac{130}{26},\frac{-48}{26}$
$x=5,\frac{-24}{13}$
Hence, $x=5$