Question 748932
let the filling rate and leaking rate of the tank p and q respectively.
without a whole it takes 5hrs
so the volume of the tank is 5p
with a whole the filling rate is (p-q) so it get additional 3 hours
so 8hrs to fill it
so the volume of tank is 8(p-q)

so {{{5p = 8(p-q)}}}
   {{{5p = 8p-8q}}}
   {{{3p = 8q}}}
   {{{p = 8q/3}}}-----------(A)

let t is the time take to empty the tank

so we can write the leaking rate = {{{volume/time}}}
{{{5p/t}}}
so this is equal to q
{{{5p/t = q}}}---------(B)
substitute p from equation A
 
{{{5*8q/3/t = q}}}
{{{t = 40/3}}}
t = 13 1/3 hours
so it will take 13 hours and 20 minutes to empty the tank