Question

Two pipes running together can fill a tank in 11 one by nine minutes if one pipe takes 5 minutes more than the the other to fill the tank separately find the time in which each pipe would fill the tank separately

Answer 1

Let the time taken by 1 pipe a be x
then pipe taken by 2nd pipe b =x+5
time taken by both pipe together 11 1/9 or 100/9
1/a+1/b=1/t
1/x+1/(x+5)=9/100
(x+5+x)/x(x+5)=100/9
100(2x+5)=9(x2+5x)
200x+500=9x2+45x
9x2-155x-500=0
9x2-180x+25x-500=0
9x(x-20)+25(x-20)=0
(x-20)(9x+25)=0
since time cannot be negative
x=20min
x+5=25min