document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132050>Question 132050</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Chuck can shovel the snow off his driveway in 40 minutes. He shovels for 20 minutes and then is joined by Joan. If they shovel the remaining snow in 10 minutes, how long would it have taken Joan to shovel the driveway alone? I don't want just the answer. If you could provide how you did it and the equations, that would be a life saver. Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96430 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=96430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If Chuck shovels the driveway in 40 minutes by himself, that means that every minute he does<BR>\n" );
document.write( "one-fortieth (1/40) of the job. Therefore, if he shovels for 20 minutes by himself he does <BR>\n" );
document.write( "20*(1/40) = 20/40 = 1/2 the job.<BR>\n" );
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document.write( "This means that when Joan starts to shovel, half the driveway is done. So the remaining amount<BR>\n" );
document.write( "of work to be done is 1/2 of the driveway. Joan shovels at some unknown rate each minute. Call<BR>\n" );
document.write( "that unknown rate J. Meanwhile Chuck continues at his rate of 1/40 per minute. So if we multiply<BR>\n" );
document.write( "these two rates by 10 minutes we get the remaining 1/2 of the driveway done. In equation form<BR>\n" );
document.write( "this is:<BR>\n" );
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document.write( "(1/40)*10 + J*10 = 1/2<BR>\n" );
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document.write( "Multiply the entire equation (all terms on both sides) by 40 to get rid of the denominator and<BR>\n" );
document.write( "the equation becomes:<BR>\n" );
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document.write( "10 + 400*J = 20<BR>\n" );
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document.write( "Get rid of the 10 on the left side by subtracting 10 from both sides and the equation is:<BR>\n" );
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document.write( "400*J = 10<BR>\n" );
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document.write( "Solve for J by dividing both sides by 400 and the equation is then reduced to:<BR>\n" );
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document.write( "J = 10/400 = 1/40<BR>\n" );
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document.write( "How interesting. Each minute Joan shovels 1/40 of the driveway, the same as Chuck does<BR>\n" );
document.write( "each minute. Therefore, if she were working alone it would also take her 40 minutes to <BR>\n" );
document.write( "shovel the entire driveway. <BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better.<BR>\n" );
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document.write( " </SPAN>\n" );
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