document.write( "Question 1058019: A B and C can clean a house in 2 hours
\n" ); document.write( "A can clean a house in 5 hours
\n" ); document.write( "B can clean a house in 6 hours
\n" ); document.write( "How long does it take A and C to clean a house?\r
\n" ); document.write( "\n" ); document.write( "My work so far:
\n" ); document.write( "A= 300/60 min.
\n" ); document.write( "B= 360/60
\n" ); document.write( "C= x/60\r
\n" ); document.write( "\n" ); document.write( "
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Algebra.Com's Answer #673028 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Their rates of cleaning would look like:
\n" ); document.write( "[ 1 house cleaned ] / [ time to clean the house ]
\n" ); document.write( "Let \"+R%5Ba%5D+\" = A's rate of cleaning
\n" ); document.write( "Let \"+R%5Bb%5D+\" = B's rate of cleaning
\n" ); document.write( "Let \"+R%5Bc%5D+\" = C's rate of cleaning
\n" ); document.write( "-----------------------------------
\n" ); document.write( "given:
\n" ); document.write( "(1) \"+R%5Ba%5D+%2B+R%5Bb%5D+%2B+R%5Bc%5D+=+1%2F2+\"
\n" ); document.write( "(2) \"+R%5Ba%5D+=+1%2F5+\"
\n" ); document.write( "(3) \"+R%5Bb%5D+=+1%2F6+\"
\n" ); document.write( "-------------------------------
\n" ); document.write( "By substitution:
\n" ); document.write( "(1) \"+1%2F5+%2B+1%2F6+%2B+R%5Bc%5D+=+1%2F2+\"
\n" ); document.write( "Multiply both sides by \"+30+\"
\n" ); document.write( "(1) \"+6+%2B+5+%2B+30R%5Bc%5D+=+15+\"
\n" ); document.write( "(1) \"+30R%5Bc%5D+=+4+\"
\n" ); document.write( "(1) \"+R%5Bc%5D+=+2%2F15+\"
\n" ); document.write( "----------------------
\n" ); document.write( "Let \"+t+\" = time in hrs for A and C together to
\n" ); document.write( "clean a house
\n" ); document.write( "\"+1%2F5+%2B+2%2F15+=+1%2Ft+\"
\n" ); document.write( "Multiply both sides by \"+15t+\"
\n" ); document.write( "\"+3t+%2B+2t+=+15+\"
\n" ); document.write( "\"+5t+=+15+\"
\n" ); document.write( "\"+t+=+3+\"
\n" ); document.write( "A and C together will take 3 hrs to clean a house
\n" ); document.write( "----------------------
\n" ); document.write( "check answer:
\n" ); document.write( "Plug this result into (1)
\n" ); document.write( "(1) \"+R%5Ba%5D+%2B+R%5Bb%5D+%2B+R%5Bc%5D+=+1%2F2+\"
\n" ); document.write( "(1) \"+%28+R%5Ba%5D+%2B+R%5Bc%5D+%29+%2B+R%5Bb%5D+=+1%2F2+\"
\n" ); document.write( "(1) \"+1%2F3+%2B+1%2F6+=+1%2F2+\"
\n" ); document.write( "(1) \"+2%2F6+%2B+1%2F6+=+3%2F6+\"
\n" ); document.write( "(1) \"+3%2F6+=+3%2F6+\"
\n" ); document.write( "OK\r
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