document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202778>Question 202778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Together, Michelle, Sal, and kristen can clean and wax a car in 1 hr 20 min. To complete the job alone, Michelle needs twice the time that Sal needs and 2 hr more than kristen. How long would it take each to clean and wax the car working alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153126 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=153126\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Together, Michelle, Sal, and kristen can clean and wax a car in 1 hr 20 min.<BR>\n" );
document.write( " To complete the job alone, Michelle needs twice the time that Sal needs<BR>\n" );
document.write( " and 2 hr more than kristen. <BR>\n" );
document.write( "How long would it take each to clean and wax the car working alone?<BR>\n" );
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document.write( "Use minutes for the time: 1 hr 20 min = 80 min; 2 hr = 120 min<BR>\n" );
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document.write( "let x = time required by Sal alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2x = Michelle's time alone<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2x-120) = Kristen's time alone <BR>\n" );
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document.write( "let the completed job = 1<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2Fx ALIGN=MIDDLE  ALT=\"80%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2F%282x%29 ALIGN=MIDDLE  ALT=\"80%2F%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2F%28%282x-120%29%29 ALIGN=MIDDLE  ALT=\"80%2F%28%282x-120%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply equation by 2x(2x-120) to clear the denominators<BR>\n" );
document.write( "80(2(2x-120) + 80(2x-120) + 80(2x) = 2x(2x-120)<BR>\n" );
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document.write( "320x - 19200 + 160x - 9600 + 160x = 4x^2 - 240x<BR>\n" );
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document.write( "320x + 160x + 160x - 19200 - 9600 = 4x^2 - 240x<BR>\n" );
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document.write( "640x - 28800 = 4x^2 - 240x<BR>\n" );
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document.write( "0 = 4x^2 - 240x - 640x + 28800  <BR>\n" );
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document.write( "0 = 4x^2 - 880x + 28800<BR>\n" );
document.write( "Simplify, divide by 4<BR>\n" );
document.write( "x^2 - 220x + 7200 = 0<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "(x - 40)(x - 180) = 0<BR>\n" );
document.write( "Two solutions,<BR>\n" );
document.write( "x = 40; does not make sense<BR>\n" );
document.write( "therefore <BR>\n" );
document.write( "x = 180 min, (3 hrs) is Sal's time alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2*180 = 360 min, (6 hrs) is Michelle's time alone<BR>\n" );
document.write( "and<BR>\n" );
document.write( "360 - 120 = 240 min, (4 hrs) is Kristen time<BR>\n" );
document.write( ";<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Check solution using 1.33 hr working together <BR>\n" );
document.write( "1.33/3 + 1.33/6 + 1.33/4<BR>\n" );
document.write( ".44 + .22 + .33 = .99 ~ 1 </SPAN>\n" );
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