Question

Two pipes running together fill a tank in \(\frac{40}{13}\) minutes if one pipe takes 3 minutes more than the other find the time taken by each pipe to fill the tank.

Answer 1

Let one pipe take x min
Then other take x + 3 min
Two pipes together can fill cistern in $\frac{40}{13}min$
Two pipes together can fill $\frac{13}{40}$ part of cistern in 1 min
One pipe can fill $\frac{1}{x}$ part of cistern in 1 min.
Other pipe can fill $\frac{1}{(x+3)}$ part of cistern in 1 min a/c to ques.
$\frac{1}{x}+\frac{1}{(x+3)}=\frac{13}{40}(2x+3)40=13(x^2+3x)80x+120=13x^2+39x0=13x^2-41x-1200=13x^2-65x+24x-1200=13x(x-5)+24(x-5)0=(x-5)(13x+24)$
either, $x=5$ or, $x=\frac{-24}{13}$
taking, x = 5
so, first pipe will take 5 mins. whereas, other will take 8 mins.