document.write( "Question 1152113: Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know that it takes 18 h using both hoses. They also know that Bob's hose, used alone, takes 70% 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 #774039 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+t+\"$ = time to fill pool with Jim's alone
\n" ); document.write( " $\"+t+-+.7t+\"$ = time to fill pool with Bob
\n" ); document.write( "--------------------------------------------------
\n" ); document.write( "Add their rates of filling to get rate filling together
\n" ); document.write( " $\"+1%2Ft+%2B+1%2F%28+t+-+.7t+%29+=+1%2F18+\"$
\n" ); document.write( "Multiply both sides by $\"+t%2A%28+.3t+%29%2A18+\"$
\n" ); document.write( " $\"+18%2A%28+.3t+%29+%2B+18t+=+t%2A%28+.3t+%29+\"$
\n" ); document.write( " $\"+5.4t+%2B+18t+=+.3t%5E2+\"$
\n" ); document.write( " $\"+.3t%5E2+-+23.4t+=+0+\"$
\n" ); document.write( " $\"+t%2A%28+.3t+-+23.4+%29+=+0+\"$
\n" ); document.write( " $\"+.3t+=+23.4+\"$
\n" ); document.write( " $\"+t+=+78+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+.3t+=+.3%2A78+\"$
\n" ); document.write( " $\"+.3t+=+23.4+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "Bob's hose alone takes 23.4 hrs
\n" ); document.write( "Jim's hose alone takes 78 hrs
\n" ); document.write( "------------------------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2Ft+%2B+1%2F%28+t+-+.7t+%29+=+1%2F18+\"$
\n" ); document.write( " $\"+1%2F78+%2B+1%2F23.4+=+1%2F18+\"$
\n" ); document.write( " $\"+.0128205+%2B+.042735+=+.055556+\"$
\n" ); document.write( " $\"+.0555555+=+.055556+\"$
\n" ); document.write( "close enough
\n" ); document.write( " \n" ); document.write( "

\n" );