document.write( "Question 686116: Working together, Bob, Sally, and Harry can dig a hole in 3.5 hours. Working alone, Harry can do it in 7 hours. Bob can do it 3/4 hours fasters than Sally. How long will it take for Sally to dig a hole alone? \n" ); document.write( "

Algebra.Com's Answer #424715 by josmiceli(19441) $\"\"$ $\"About$

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Add their rates of working to get their time
\n" ); document.write( "working together
\n" ); document.write( " $\"+b+\"$ = Bob's time to dig hole in hours working alone
\n" ); document.write( " $\"+s+\"$ = Sally's time to dig hole in hours working alone
\n" ); document.write( " $\"+h+\"$ = Harry's time to dig hole in hours working alone
\n" ); document.write( "-------------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+1%2Fb+%2B+1%2Fs+%2B+1%2Fh+=+1%2F3.5+\"$
\n" ); document.write( "(2) $\"+h+=+7+\"$
\n" ); document.write( "(3) $\"+b+=+s+-+.75+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "Substitute (2) and (3) into (1)
\n" ); document.write( "(1) $\"+1%2F%28+s+-+.75%29+%2B+1%2Fs+%2B+1%2F7+=+2%2F7+\"$
\n" ); document.write( "(1) $\"+1%2F%28+s+-+.75%29+%2B+1%2Fs+=+1%2F7+\"$
\n" ); document.write( "Multiply both sides by $\"+7s%2A%28+s+-+.75+%29+\"$
\n" ); document.write( "(1) $\"+7s+%2B+7%2A%28+s+-+.75+%29+=+s%2A%28+s+-+.75+%29+\"$
\n" ); document.write( "(1) $\"+7s+%2B+7s+-+5.25+=+s%5E2+-+.75s+\"$
\n" ); document.write( "(1) $\"+s%5E2+-+14.75s+%2B+5.25+=+0+\"$
\n" ); document.write( "Solve using quadratic equation
\n" ); document.write( " $\"+s+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( " $\"+b+=+-14.75+\"$
\n" ); document.write( " $\"+c+=+5.25+\"$
\n" ); document.write( " $\"+s+=+%28-%28-14.75%29+%2B-+sqrt%28+%28-14.75%29%5E2+-+4%2A1%2A5.25+%29%29+%2F+%282%2A1%29+\"$
\n" ); document.write( " $\"+s+=+%28+14.75+%2B-+sqrt%28+217.5625+-+21+%29%29+%2F+2+\"$
\n" ); document.write( " $\"+s+=+%28+14.75+%2B-+sqrt%28+196.5625+%29%29+%2F+2+\"$
\n" ); document.write( " $\"+s+=+%28+14.75+%2B-+14.020075%29+%2F+2+\"$
\n" ); document.write( " $\"+s+=+%28+14.75+%2B+14.020075%29+%2F+2+\"$
\n" ); document.write( " $\"+s+=+28.77007+%2F+2+\"$
\n" ); document.write( " $\"+s+=+14.38504+\"$
\n" ); document.write( " $\"+.38504%2A60+=+23.1+\"$
\n" ); document.write( "Sally can dig the hole alone in
\n" ); document.write( "14 hrs and 23 min
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+1%2Fb+%2B+1%2F14.385+%2B+1%2F7+=+1%2F3.5+\"$
\n" ); document.write( " $\"+b+=+s+-+.75+\"$
\n" ); document.write( " $\"+b+=+14.385+-+.75+\"$
\n" ); document.write( " $\"+b+=+13.635+\"$
\n" ); document.write( "(1) $\"+1%2F13.635+%2B+1%2F14.385+%2B+1%2F7+=+1%2F3.5+\"$
\n" ); document.write( "(1) $\"+.07334+%2B+.06952+%2B+.14286+=+.28571+\"$
\n" ); document.write( "(1) $\"+.28572+=+.28571+\"$
\n" ); document.write( "I think error is due to rounding off
\n" ); document.write( "OK\r
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