document.write( "Question 966399: Working alone, Ryan can dig a 10ft by 10ft hole in 5 hours. Castle can dig the same hole in six hours. How long word it take them if they worked together? \n" ); document.write( "

Algebra.Com's Answer #590664 by josmiceli(19441) $\"\"$ $\"About$

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Add their rates of working:
\n" ); document.write( "Ryan's rate:
\n" ); document.write( "[ 1 hole dug ] / [ 5 hrs ]
\n" ); document.write( "Castle's rate:
\n" ); document.write( "[ 1 hole dug ] / [ 6 hrs ]
\n" ); document.write( "------------------------
\n" ); document.write( "Let $\"+t+\"$ = their time in hrs working together
\n" ); document.write( " $\"+1%2F5+%2B+1%2F6+=+1%2Ft+\"$
\n" ); document.write( "Multiply both sides by $\"+30t+\"$
\n" ); document.write( " $\"+6t+%2B+5t+=+30+\"$
\n" ); document.write( " $\"+11t+=+30+\"$
\n" ); document.write( " $\"+t+=+2.727+\"$
\n" ); document.write( " $\"+.727%2A60+=+44+\"$
\n" ); document.write( "It will take them 2 hrs 44 min working together
\n" ); document.write( "-------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2F5+%2B+1%2F6+=+1%2Ft+\"$
\n" ); document.write( " $\"+1%2F5+%2B+1%2F6+=+1%2F2.727+\"$
\n" ); document.write( " $\"+.2+%2B+.1667+=+.3667+\"$
\n" ); document.write( " $\"+.3667+=+.3667+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );