document.write( "Question 882375: Can't solve this question please help.\r
\n" ); document.write( "\n" ); document.write( "- Abby, Barry and Crystal are artists painting a mural. Working together it takes them 6 days to complete the entire painting. While working, they notice that Abby paints 3 times faster than Crystal, and Barry paints 1.5 times faster than Crystal. How long would it have taken Crystal to paint the mural alone? \n" ); document.write( "
Algebra.Com's Answer #532804 by josmiceli(19441)\"\" \"About 
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Add their rates of working to get
\n" ); document.write( "their rate working together
\n" ); document.write( "Let \"+R%5BA%5D+\" = Abby's rate
\n" ); document.write( "Let \"+R%5BB%5D+\" = Barry's rate
\n" ); document.write( "Let \"+R%5BC%5D+\" = Crystal's rate
\n" ); document.write( "Their rate working together is
\n" ); document.write( "( 1 mural ) / ( 6 days ), so
\n" ); document.write( "(1) \"+R%5BA%5D+%2B+R%5BB%5D+%2B+R%5BC%5D+=+1%2F6+\"
\n" ); document.write( "Also given:
\n" ); document.write( "(2) \"+R%5BA%5D+=+3%2AR%5BC%5D+\"
\n" ); document.write( "(3) \"+R%5BB%5D+=+1.5%2AR%5BC%5D+\"
\n" ); document.write( "----------------------
\n" ); document.write( "Substitute (2) and (3) into (1)
\n" ); document.write( "(1) \"+3%2AR%5BC%5D+%2B+%283%2F2%29%2AR%5BC%5D+%2B+R%5BC%5D+=+1%2F6+\"
\n" ); document.write( "(1) \"+%2811%2F2%29%2AR%5BC%5D+=+1%2F6+\"
\n" ); document.write( "(1) \"+R%5BC%5D+=+2%2F66+\"
\n" ); document.write( "(1) \"+R%5BC%5D+=+1%2F33+\"
\n" ); document.write( "Crystal would have taken 33 days to
\n" ); document.write( "paint the mural working alone
\n" ); document.write( "----------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) \"+R%5BA%5D+=+3%2AR%5BC%5D+\"
\n" ); document.write( "(2) \"+R%5BA%5D+=+3%2A%281%2F33%29+\"
\n" ); document.write( "(2) \"+R%5BA%5D+=+1%2F11+\"
\n" ); document.write( "and
\n" ); document.write( "(3) \"+R%5BB%5D+=+1.5%2AR%5BC%5D+\"
\n" ); document.write( "(3) \"+R%5BB%5D+=+%283%2F2%29%2A%281%2F33%29+\"
\n" ); document.write( "(3) \"+R%5BB%5D+=+1%2F22+\"
\n" ); document.write( "---------------------
\n" ); document.write( "and, from (3):
\n" ); document.write( "(1) \"+R%5BA%5D+%2B+R%5BB%5D+%2B+R%5BC%5D+=+1%2F6+\"
\n" ); document.write( "(1) \"+1%2F11+%2B+1%2F22+%2B+1%2F33+=+1%2F6+\"
\n" ); document.write( "(1) \"+6%2F66+%2B+3%2F66+%2B+2%2F66+=+1%2F6+\"
\n" ); document.write( "(1) \"+11%2F66+=+1%2F6+\"
\n" ); document.write( "(1) \"+1%2F6+=+1%2F6+\"
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "
\n" );