document.write( "Question 397853: Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes 24 h using both hoses. They also know that Bob's hose, used alone, takes 40% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone? \n" ); document.write( "
Algebra.Com's Answer #281873 by josmiceli(19441)\"\" \"About 
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Let \"1%2Fb\" = rate that Bob's hose alone fills pool (1 pool/ b hrs)
\n" ); document.write( "Let \"1%2Fj\" = rate that Jim's hose alone fills pool (1 pool/ j hrs)
\n" ); document.write( "Let \"1%2Fx\" = rate that both hoses fill pool (1 pool/ x hrs)
\n" ); document.write( "Then
\n" ); document.write( "(1) \"1%2Fb+%2B+1%2Fj+=+1%2Fx\"
\n" ); document.write( "-----------------
\n" ); document.write( "given:
\n" ); document.write( "\"1%2Fx+=+1%2F24\" (1 pool)/(24 hrs)
\n" ); document.write( "\"1%2Fb+=+1%2F%28j+-+.4j%29\"
\n" ); document.write( "(2) \"1%2Fb=+1%2F%28.6j%29\"
\n" ); document.write( "and, from (1)
\n" ); document.write( "(1) \"1%2Fb+%2B+1%2Fj+=+1%2F24\"
\n" ); document.write( "These are 2 equations and 2 unknowns, so it's solvable
\n" ); document.write( "By substitution:
\n" ); document.write( "\"1%2F%28.6j%29+%2B+1%2Fj+=+1%2F24\"
\n" ); document.write( "Multiply both sides by \".6j\"
\n" ); document.write( "\"1+%2B+.6+=+%28.6j%29%2F24\"
\n" ); document.write( "\".6j+=+24+%2B+14.4\"
\n" ); document.write( "\"j+=+38.4%2F.6\"
\n" ); document.write( "\"j+=+64\"
\n" ); document.write( "and, from (2),
\n" ); document.write( "\"1%2Fb+=+1%2F%28.6%2A64%29\"
\n" ); document.write( "\"1%2Fb+=+1%2F38.4\"
\n" ); document.write( "\"b+=+38.4\"
\n" ); document.write( "Bob's hose alone takes 38.4 hrs
\n" ); document.write( "Jim's hose alone takes 64 hrs
\n" ); document.write( "-------------------------
\n" ); document.write( "check answer:
\n" ); document.write( "(1) \"1%2Fb+%2B+1%2Fj+=+1%2F24\"
\n" ); document.write( "\"1%2F38.4+%2B+1%2F64+=+1%2F24\"
\n" ); document.write( "\"1%2F384+%2B+1%2F640+=+1%2F240\"
\n" ); document.write( "I'll just convert to decimals:
\n" ); document.write( "\".002604167+%2B+.0015625+=+.00416667\"
\n" ); document.write( "\".004166667+=+.00416667\"
\n" ); document.write( "close enough
\n" ); document.write( " \n" ); document.write( "
\n" );