document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106209>Question 106209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A passenger train can travel 325 mi in the same time a freight train takes to travel 200 mi.  If the speed of the passenger train is 25 mi/h faster than the speed of the freight train, find the speed of each. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77255 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=77255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve this problem, use the distance formula:<BR>\n" );
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document.write( "D = R*T<BR>\n" );
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document.write( "where D represents the distance traveled, R represents the rate or speed, and T represents<BR>\n" );
document.write( "the amount of Time that the travel takes place.<BR>\n" );
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document.write( "Before you begin recognize that if the speed of the freight train is F mph, then the speed of<BR>\n" );
document.write( "the passenger train is F + 25 mph.<BR>\n" );
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document.write( "Now we can write two equations. The distance that the passenger train travels is 325 miles.<BR>\n" );
document.write( "The speed at which it travels is F + 25. And the time it travels is T. So its equation is:<BR>\n" );
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document.write( "325 = (F+25)*T<BR>\n" );
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document.write( "And the distance that the freight train travels is 200 miles. Its speed is F. And the time<BR>\n" );
document.write( "it travels is also T. So its distance equation is:<BR>\n" );
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document.write( "200 = F*T<BR>\n" );
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document.write( "Suppose we solved both these equations for T. In the first equation we would divide both<BR>\n" );
document.write( "sides by (F+25) and we would get that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+325%2F%28F%2B25%29 ALIGN=MIDDLE  ALT=\"T+=+325%2F%28F%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In the second equation we would solve for T by dividing both sides by F to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+200%2FF ALIGN=MIDDLE  ALT=\"T+=+200%2FF\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But the problem tells us that the two times ... the time the passenger train travels<BR>\n" );
document.write( "is the same amount of time as the freight train travels. Therefore the two left sides (which<BR>\n" );
document.write( "are both T) are equal. Therefore, we know that the two right sides must be equal also. So<BR>\n" );
document.write( "we can set the two right sides equal and this equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=325%2F%28F%2B25%29+=+200%2FF ALIGN=MIDDLE  ALT=\"325%2F%28F%2B25%29+=+200%2FF\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28F%2B25%29%2AF ALIGN=MIDDLE  ALT=\"%28F%2B25%29%2AF\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28F%2B25%29%2AF%2A+325%29%2F%28F%2B25%29+=+%28%28F%2B25%29%2AF%2A200%29%2FF ALIGN=MIDDLE  ALT=\"%28%28F%2B25%29%2AF%2A+325%29%2F%28F%2B25%29+=+%28%28F%2B25%29%2AF%2A200%29%2FF\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cancel the terms in the numerators with the same term in the denominator:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28F%2B25%29%2AF%2A+325%29%2Fcross%28F%2B25%29+=+%28%28F%2B25%29%2Across%28F%29%2A200%29%2Fcross%28F%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the equation reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=325F+=+200%28F%2B25%29 ALIGN=MIDDLE  ALT=\"325F+=+200%28F%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply out the right side by multiplying 200 times each of the terms in the parentheses<BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=325F+=+200F+%2B+5000 ALIGN=MIDDLE  ALT=\"325F+=+200F+%2B+5000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 200F on the right side by subtracting 200F from both sides to reduce the<BR>\n" );
document.write( "equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125F+=+5000 ALIGN=MIDDLE  ALT=\"125F+=+5000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for F by dividing both sides by 125 and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+5000%2F125+=+40 ALIGN=MIDDLE  ALT=\"F+=+5000%2F125+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This tells you that the speed of the freight train is 40 mph. Since the speed of the passenger<BR>\n" );
document.write( "train is 25 mph faster, its speed is 40 + 25 = 65 mph.<BR>\n" );
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document.write( "You can check these answers by noting that at 40 mph it will take the freight train 5<BR>\n" );
document.write( "hours to go 200 miles. And at 65 mph in 5 hours the passenger train goes 5 * 65 = 325 miles.<BR>\n" );
document.write( "Everything checks.<BR>\n" );
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document.write( "Hope this helps you to understand this problem and shows you a way of working through it<BR>\n" );
document.write( "to get the answer.<BR>\n" );
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