document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1056463>Question 1056463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a really hard time answering this word problem. Here it is:\r<BR>\n" );
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document.write( "Two sisters washed the family car in 24 min. When they each washed the car alone, the older sister took 10 min longer to do the job than the younger sister. How would the younger  sister take to wash the car alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #671568 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=671568\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the younger sister's time=x<BR>\n" );
document.write( "the older sister's time is x+10<BR>\n" );
document.write( "in 1 minute, the younger sister does 1/x of the car and the older sister does 1/(x+10) of the car.<BR>\n" );
document.write( "in 24 minutes, they do the whole car together.<BR>\n" );
document.write( "Therefore 24/x+24/(x+10)=1 (the whole car)<BR>\n" );
document.write( "Multiply by x(x+10) both sides to clear fractions<BR>\n" );
document.write( "24(x+10)+24x=x^2+10x, which is x(x+10)<BR>\n" );
document.write( "x^2+10x=24x+240+24x<BR>\n" );
document.write( "x^2-38x-240=0<BR>\n" );
document.write( "x=(1/2)(38+/-sqrt(38^2+960); sqrt term is of (2404)=49.03<BR>\n" );
document.write( "Therefore, the one positive root is (1/2)87.03=43.52 min<BR>\n" );
document.write( "43.5 min for the younger sister ANSWER<BR>\n" );
document.write( "53.5 min for the older sister<BR>\n" );
document.write( "(24/43.5)=0.55<BR>\n" );
document.write( "(24/53.5)=0.45 </SPAN>\n" );
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