![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
A backyard swimming pool has two fill pipes and a drain pipe.
\n" ); document.write( " The pool fills in 9 hours with the first fill pipe.
\n" ); document.write( " Draining the pool with the drain pipe takes 1 hour longer than filling the pool with the second fill pipe.
\n" ); document.write( " If all three pipes are open at once, the pool can be filled in 8 hours.
\n" ); document.write( " How many hours would draining the pool take with the two fill pipes closed?
\n" ); document.write( ":
\n" ); document.write( "let d = time for the drain to empty the pool, when the other two pipes are closed.
\n" ); document.write( "then
\n" ); document.write( "(d-1) = time for the 2nd pipe to fill the pool
\n" ); document.write( ":
\n" ); document.write( "Let the filled pool = 1
\n" ); document.write( "
\n" ); document.write( "multiply equation by 9d(d-1), cancel the denominators, resulting in
\n" ); document.write( "8d(d-1) + 9d(8) - 9(d-1)(8) = 9d(d-1)
\n" ); document.write( "8d^2 - 8d + 72d - 72d + 72 = 9d^2 - 9d
\n" ); document.write( "8d^2 - 8d + 72 = 9d^2 - 9d
\n" ); document.write( "combine like terms on the right
\n" ); document.write( "0 = 9d^2 - 8d^2 - 9d + 8d - 72
\n" ); document.write( "d^2 - d - 72 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(d-9(d+8) = 0
\n" ); document.write( "The positive solution
\n" ); document.write( "d = 9 hrs to drain the pool
\n" ); document.write( ":
\n" ); document.write( "See if the works
\n" ); document.write( "