SOLUTION: A cistern can be filled in 9 hours but it takes 10 hours due to a leak in its bottom.If the cistern full,then the time the tank leak will take to empty it is

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A cistern can be filled in 9 hours but it takes 10 hours due to a leak in its bottom.If the cistern full,then the time the tank leak will take to empty it is      Log On


   

Question 777946: A cistern can be filled in 9 hours but it takes 10 hours due to a leak in its bottom.If the cistern full,then the time the tank leak will take to empty it is
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rate of filling is:
( 1 tank ) / ( 9 hrs )
Let +-R+ = the rate that the leak empties the tank
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Starting with an empty tank, add the rates to get
the total rate needed to fill the tank
+1%2F9+-+R+=+1%2F10+
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+R+=+1%2F9+-+1%2F10+
+R+=+10%2F90+-+9%2F90+
+R+=+1%2F90+
The rate of leaking is ( 1 tank ) / ( 90 hrs )
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So, if the tank is full, the tank will empty in 90 hrs