SOLUTION: math question - a hose can fill a swimming pool in 50 minutes. the pool leaks at a steady rate that drains completely in 300 minutes, how many minutes will it take the hose to fill

Question 862331: math question - a hose can fill a swimming pool in 50 minutes. the pool leaks at a steady rate that drains completely in 300 minutes, how many minutes will it take the hose to fill the leaky pool?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the equation to use is RT=Q
this means rate * time = quantity of work produced.
Q = 1 which is 1 pool
to fill the pool, the equation is R*50 = 1 which makes R = 1/50.
the pool fills at the rate of 1/50 of the pool each minute.
to empty the pool, the equation is R*300 = 1 which makes R = 1/300.
the pool empties at the rate of 1/300 of the pool each minute.
if you start with an empty pool, then for each minute, 1/50 of the pool will be filled and 1/300 of the pool will be emptied, assuming the fill and empty rates stay the same throughout.
that's a net fill rate of 1/50 - 1/300 which is equal to 6/300 - 1/300 which is equal to 5/300.
for net fill rate is therefore 5/300 of the pool per minute.
the same equation applies, only this time R is known and we can solve for T.
5/300 * T = 1 is the equation we start with:
multiply booth sides of this equation by 300 to get 5 * T = 300
divide both sides of this equation by 5 to get T = 300/5 = 60 minutes.
the pool will be filled in 60 minutes.
since T = 60 minutes, the gross fill rate is 1/50 of the pool per minute to make 60/50 of the pool full in 60 minutes, and the gross empty rate is 1/300 of the pool per minute to make 60/300 of the pool empty in 60 minutes.
60/50 - 60/300 = 360 / 300 - 60/300 = 300/300 = 1.
the net effect of filling at the rate of 1/50 of the pool per minute and emptying at the rate of 1/300 of the pool per minute gets you 1 full pool after 60 minutes.

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