SOLUTION: A tap can fill a water tank in 5 hrs, but there is whole in the tank....so it takes 3 hrs more to fill it.......if the tap is closed after filling the tank...how much time the whol

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A tap can fill a water tank in 5 hrs, but there is whole in the tank....so it takes 3 hrs more to fill it.......if the tap is closed after filling the tank...how much time the whol      Log On


   

Question 748932: A tap can fill a water tank in 5 hrs, but there is whole in the tank....so it takes 3 hrs more to fill it.......if the tap is closed after filling the tank...how much time the whole will take to empty the filled tank??????????
Answer by nilan(17) About Me  (Show Source):
You can put this solution on YOUR website!
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%28p-q%29
5p+=+8p-8q
3p+=+8q
p+=+8q%2F3-----------(A)
let t is the time take to empty the tank
so we can write the leaking rate = volume%2Ftime
5p%2Ft
so this is equal to q
5p%2Ft+=+q---------(B)
substitute p from equation A

5%2A8q%2F3%2Ft+=+q
t+=+40%2F3
t = 13 1/3 hours
so it will take 13 hours and 20 minutes to empty the tank