document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115248>Question 115248</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 108 miles in the same time that Dana travels 99 miles. If Chuck's rate of travel is 3 mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83830 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=83830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the formula that Distance equals Speed times Time to solve this equation. In equation<BR>\n" );
document.write( "form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+S%2AT ALIGN=MIDDLE  ALT=\"D+=+S%2AT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "For Chuck, the distance he traveled was 108 miles. His speed was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bc%5D ALIGN=MIDDLE  ALT=\"S%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the \"c\" indicates<BR>\n" );
document.write( "it is Chuck's speed. Substituting these into the equation for chuck results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108+=+S%5Bc%5D%2AT ALIGN=MIDDLE  ALT=\"108+=+S%5Bc%5D%2AT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve this equation for T by dividing both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bc%5D ALIGN=MIDDLE  ALT=\"S%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+108%2FS%5Bc%5D ALIGN=MIDDLE  ALT=\"T+=+108%2FS%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Meanwhile, Dana travels 99 miles in the same time. Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bd%5D ALIGN=MIDDLE  ALT=\"S%5Bd%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > represent Dana's speed. <BR>\n" );
document.write( "Substituting these values into the distance equation results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99+=+S%5Bd%5D%2AT ALIGN=MIDDLE  ALT=\"99+=+S%5Bd%5D%2AT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve this equation for T by dividing both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bd%5D ALIGN=MIDDLE  ALT=\"S%5Bd%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+99%2FS%5Bd%5D ALIGN=MIDDLE  ALT=\"T+=+99%2FS%5Bd%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So we have two equations for T ... one for Chuck and one for Dana. But, according <BR>\n" );
document.write( "to the problem, both drivers drive for equal times. So the two T equations are equal. That<BR>\n" );
document.write( "means the right sides of these equations are equal for the two drivers. So it can be said<BR>\n" );
document.write( "that:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2FS%5Bc%5D+=+99%2FS%5Bd%5D ALIGN=MIDDLE  ALT=\"108%2FS%5Bc%5D+=+99%2FS%5Bd%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next the problem tells you that Chuck's speed is 3 miles per hour more than Dana's. So<BR>\n" );
document.write( "it also can be said that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bc%5D+=+S%5Bd%5D+%2B+3 ALIGN=MIDDLE  ALT=\"S%5Bc%5D+=+S%5Bd%5D+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute the right side of this into the Time equation and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2F%28S%5Bd%5D%2B3%29+=+99%2FS%5Bd%5D ALIGN=MIDDLE  ALT=\"108%2F%28S%5Bd%5D%2B3%29+=+99%2FS%5Bd%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Put both of these fractions over a common denominator by multiplying both sides of this <BR>\n" );
document.write( "equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28S%5Bd%5D%2A%28S%5Bd%5D+%2B3%29%29%2F%28S%5Bd%5D%2A%28S%5Bd%5D+%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28S%5Bd%5D%2A%28S%5Bd%5D+%2B3%29%29%2F%28S%5Bd%5D%2A%28S%5Bd%5D+%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note that since the numerator of this<BR>\n" );
document.write( "multiplier is equal to the denominator, this is equivalent to multiplying both sides of the<BR>\n" );
document.write( "equation by 1.<BR>\n" );
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document.write( "This multiplication leads to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28S%5Bd%5D%2A%28S%5Bd%5D+%2B3%29%29%2F%28S%5Bd%5D%2A%28S%5Bd%5D+%2B3%29%29%29%2A%28108%2F%28S%5Bd%5D%2B3%29%29+=+%28%28S%5Bd%5D%2A%28S%5Bd%5D+%2B3%29%29%2F%28S%5Bd%5D%2A%28S%5Bd%5D+%2B3%29%29%29%2A%2899%2FS%5Bd%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Cancel the like terms in the denominators and numerators on both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28S%5Bd%5D%2A%28cross%28S%5Bd%5D+%2B3%29%29%29%2F%28S%5Bd%5D%2A%28S%5Bd%5D+%2B3%29%29%29%2A%28108%2Fcross%28S%5Bd%5D%2B3%29%29+=+%28%28%28cross%28S%5Bd%5D%29%29%2A%28S%5Bd%5D+%2B3%29%29%2F%28S%5Bd%5D%2A%28S%5Bd%5D+%2B3%29%29%29%2A%2899%2F%28cross%28S%5Bd%5D%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This leaves:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28108%2AS%5Bd%5D%29%2F%28S%5Bd%5D%2A%28S%5Bd%5D+%2B3%29%29=+%2899%2A%28S%5Bd%5D%2B+3%29%29%2F%28S%5Bd%5D%2A%28S%5Bd%5D+%2B3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since the denominators are the same on both sides, the numerators must be equal. So, setting<BR>\n" );
document.write( "the numerators equal results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2AS%5Bd%5D=+99%2A%28S%5Bd%5D%2B3%29 ALIGN=MIDDLE  ALT=\"108%2AS%5Bd%5D=+99%2A%28S%5Bd%5D%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiplying out the right side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2AS%5Bd%5D+=+99%2AS%5Bd%5D+%2B+297 ALIGN=MIDDLE  ALT=\"108%2AS%5Bd%5D+=+99%2AS%5Bd%5D+%2B+297\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99%2AS%5Bd%5D ALIGN=MIDDLE  ALT=\"99%2AS%5Bd%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides to get rid of that term on the right side and the<BR>\n" );
document.write( "result is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2AS%5Bd%5D+=+297 ALIGN=MIDDLE  ALT=\"9%2AS%5Bd%5D+=+297\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bd%5D ALIGN=MIDDLE  ALT=\"S%5Bd%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > by dividing both sides by 9 to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bd%5D+=+297%2F9+=+33 ALIGN=MIDDLE  ALT=\"S%5Bd%5D+=+297%2F9+=+33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So Dana's speed is 33 miles per hour. And Chuck's speed, which is 3 miles per hour faster,<BR>\n" );
document.write( "is 36 miles per hour.<BR>\n" );
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document.write( "Check. At 36 miles per hour it will take Chuck 3 hours to go 108 miles. And at 33 miles per<BR>\n" );
document.write( "hour, it will take Dana 3 hours to go 99 miles. The answer checks because the times are equal.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and to see how it might be solved.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );