document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159703>Question 159703</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train travels 180 miles in the same time that a car travels 120 miles. The speed of the train is 20 miles per hour faster than the speed of the car. Find the speed of the train and the speed of the car. Please solve step by step. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117768 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=117768\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > and therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=d%2Fr ALIGN=MIDDLE  ALT=\"t=d%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Now, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bt%5D ALIGN=MIDDLE  ALT=\"d%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D ALIGN=MIDDLE  ALT=\"r%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the distance travelled and the speed of the train, while <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bc%5D ALIGN=MIDDLE  ALT=\"d%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bc%5D ALIGN=MIDDLE  ALT=\"r%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the distance travelled and the speed of the car, then:\r<BR>\n" );
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document.write( "We are given that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bt%5D=180 ALIGN=MIDDLE  ALT=\"d%5Bt%5D=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bc%5D=120 ALIGN=MIDDLE  ALT=\"d%5Bc%5D=120\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D=r%5Bc%5D%2B20 ALIGN=MIDDLE  ALT=\"r%5Bt%5D=r%5Bc%5D%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Further, we know that the time is the same for both the train's trip and the car's trip.\r<BR>\n" );
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document.write( "For the train:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=180%2Fr%5Bt%5D ALIGN=MIDDLE  ALT=\"t=180%2Fr%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=180%2F%28r%5Bc%5D%2B20%29 ALIGN=MIDDLE  ALT=\"t=180%2F%28r%5Bc%5D%2B20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and\r<BR>\n" );
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document.write( "For the car:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=120%2Fr%5Bc%5D ALIGN=MIDDLE  ALT=\"t=120%2Fr%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=t ALIGN=MIDDLE  ALT=\"t=t\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2F%28r%5Bc%5D%2B20%29=120%2Fr%5Bc%5D ALIGN=MIDDLE  ALT=\"180%2F%28r%5Bc%5D%2B20%29=120%2Fr%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cross-multiply:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180r%5Bc%5D=120%28r%5Bc%5D%2B20%29 ALIGN=MIDDLE  ALT=\"180r%5Bc%5D=120%28r%5Bc%5D%2B20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180r%5Bc%5D=120r%5Bc%5D%2B2400 ALIGN=MIDDLE  ALT=\"180r%5Bc%5D=120r%5Bc%5D%2B2400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-120r%5Bc%5D ALIGN=MIDDLE  ALT=\"-120r%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180r%5Bc%5D-120r%5Bc%5D=2400 ALIGN=MIDDLE  ALT=\"180r%5Bc%5D-120r%5Bc%5D=2400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Collect like terms:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60r%5Bc%5D=2400 ALIGN=MIDDLE  ALT=\"60r%5Bc%5D=2400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide by 60: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bc%5D=40 ALIGN=MIDDLE  ALT=\"r%5Bc%5D=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Compute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D ALIGN=MIDDLE  ALT=\"r%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bt%5D=r%5Bc%5D%2B20=40%2B20=60 ALIGN=MIDDLE  ALT=\"r%5Bt%5D=r%5Bc%5D%2B20=40%2B20=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the train travels at 60 mph and the car at 40 mph.\r<BR>\n" );
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document.write( "Check the answer:\r<BR>\n" );
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document.write( "How long does it take the train to go 180 miles?  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2F60=3 ALIGN=MIDDLE  ALT=\"180%2F60=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours\r<BR>\n" );
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document.write( "How long does it take the car to go 120 miles?  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2F40=3 ALIGN=MIDDLE  ALT=\"120%2F40=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours.\r<BR>\n" );
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document.write( "The time is the same so the answer checks. </SPAN>\n" );
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