document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=972443>Question 972443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Some travelers went 3 hours by car and 5 hours by train, passing 510 km during the whole ride. We know that they went 90 kilometers more by train than by car. Find the rate of the train and the rate of the car. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #594814 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=594814\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Some travelers went 3 hours by car and 5 hours by train, passing 510 km during the whole ride.<BR>\n" );
document.write( " We know that they went 90 kilometers more by train than by car.<BR>\n" );
document.write( " Find the rate of the train and the rate of the car.<BR>\n" );
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document.write( "let c = rate of the car<BR>\n" );
document.write( "let t = rate of the train<BR>\n" );
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document.write( "Write a distance equation<BR>\n" );
document.write( "\" 3 hours by car and 5 hours by train, passing 510 km during the whole ride. \"<BR>\n" );
document.write( "3c + 5t = 510<BR>\n" );
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document.write( "\"they went 90 kilometers more by train than by car.\"<BR>\n" );
document.write( "5t - 3c = 90<BR>\n" );
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document.write( "Arrange the two equations for elimination<BR>\n" );
document.write( "5t + 3c = 510<BR>\n" );
document.write( "5t - 3c = 90<BR>\n" );
document.write( "---------------Addition eliminates c, find t<BR>\n" );
document.write( "10t + 0 = 600<BR>\n" );
document.write( "t = 600/10<BR>\n" );
document.write( "t = 60 km/hr is the rate of the train<BR>\n" );
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document.write( "Use the 1st equation to find c, replace t with 60<BR>\n" );
document.write( "3c + 5(60) = 510<BR>\n" );
document.write( "3c + 300 = 510<BR>\n" );
document.write( "3c = 510 - 300<BR>\n" );
document.write( "3c = 210<BR>\n" );
document.write( "c = 210/3<BR>\n" );
document.write( "c = 70 km/hr is the rate of the car<BR>\n" );
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document.write( "Check this in the 2nd equation; replace t and c<BR>\n" );
document.write( "5(60) - 3(70) = 90<BR>\n" );
document.write( "300 - 210 = 90\r<BR>\n" );
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document.write( " </SPAN>\n" );
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