document.write( "Question 640140: Hi, having difficulty with a problem in math.
\n" ); document.write( "When a drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened it takes 5 hours to empty the pool. The pool is being filled, but the drain was accidently left open. How long until the pool is filled? \n" ); document.write( "
Algebra.Com's Answer #403041 by DrBeeee(684)\"\" \"About 
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Let G = the capacity of the pool.
\n" ); document.write( "Let r = fill rate in gallons/hour
\n" ); document.write( "Let d = drain rate in gallons/hour
\n" ); document.write( "Then G = rate*time, where time is hours.
\n" ); document.write( "From the first statement, we fill the pool in 4 hours, we have
\n" ); document.write( "(1) G = r*4
\n" ); document.write( "And drain statement we have
\n" ); document.write( "(2) G = d*5
\n" ); document.write( "When we fill with the drain open the net fill rate is
\n" ); document.write( "(3) net rate = (r-d) gal/hr
\n" ); document.write( "Let T = the time to fill with the drain open, then we have
\n" ); document.write( "(4) G = (r-d)*T
\n" ); document.write( "Substitute (1) and (2) into (4) yields
\n" ); document.write( "(5) G = (G/4 - G/5)*T
\n" ); document.write( "Note that G cancels, giving
\n" ); document.write( "T = 1/(1/4 - 1/5) or
\n" ); document.write( "T = 1/((5-4)/20) or
\n" ); document.write( "(6) T = 20
\n" ); document.write( "Answer: When the drain is open, it will take 20 hours to fill the pool.
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