document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140094>Question 1140094</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I figure when two motorcycles will meet when they are 196 apart, one is going 65 mph one is going 75 mph I figured the time for both riders but how do I figure when they will meet? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760577 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=760577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r * t = d\r<BR>\n" );
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document.write( "r = rate<BR>\n" );
document.write( "t = time<BR>\n" );
document.write( "d = distance\r<BR>\n" );
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document.write( "the distance between the motorcyclists is equal to 196 miles.\r<BR>\n" );
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document.write( "the rate for one of the motorcyclists is equal to 65 miles per hour.\r<BR>\n" );
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document.write( "the rate for the other motorcyclist is equal to 75 miles per hour.\r<BR>\n" );
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document.write( "the time that each motorcyclist travels has to be the same.\r<BR>\n" );
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document.write( "since the total distance is 196 miles, one of the motorcyclists will travel x miles and the other motorcyclist will travel 196 - x miles.\r<BR>\n" );
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document.write( "you can choose for yourself which one travels x miles and which one travels 196 - x miles.\r<BR>\n" );
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document.write( "note that the total distance traveled by both will be 196 miles because x + 196 - x = 196.\r<BR>\n" );
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document.write( "the general formula is, once again, r * t = d\r<BR>\n" );
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document.write( "your formula for the first motorcyclist becomes:\r<BR>\n" );
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document.write( "65 * t = x\r<BR>\n" );
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document.write( "your formula for the second motorcyclist becomes:\r<BR>\n" );
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document.write( "75 * t = 196 - x\r<BR>\n" );
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document.write( "these two equations need to be solved simultaneously so the value of x and t will be the same in both equations.\r<BR>\n" );
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document.write( "the trick is to make one of the variables disappear so that you can solve for the other variable.\r<BR>\n" );
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document.write( "once you find the value of the other variable, you can use that value to find the value of the variable that disappeared.\r<BR>\n" );
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document.write( "this is standard procedure for solving equations simultaneously.\r<BR>\n" );
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document.write( "there are several ways to do it.\r<BR>\n" );
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document.write( "here's a reference on how to solve equations simultaneously.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/systlin1.htm\" target = \"_blank\">https://www.purplemath.com/modules/systlin1.htm</a>\r<BR>\n" );
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document.write( "i'm going to solve this one by substitution.\r<BR>\n" );
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document.write( "your two equations are:\r<BR>\n" );
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document.write( "65 * t = x<BR>\n" );
document.write( "75 * t = 196 - x\r<BR>\n" );
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document.write( "in the first equation,solve for t to get t = x / 65\r<BR>\n" );
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document.write( "in the second equation, replace t with x / 65 to get:\r<BR>\n" );
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document.write( "75 * x / 65 = 196 - x\r<BR>\n" );
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document.write( "multiply both sides of this equation by 65 to get:\r<BR>\n" );
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document.write( "75 * x = 65 * (196 - x)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "75 * x = 12740 - 65 * x\r<BR>\n" );
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document.write( "add 65 * x to both sides of this equation to get:\r<BR>\n" );
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document.write( "75 * x + 65 * x = 12740\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "140 * x = 12740\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 12740 / 140 = 91\r<BR>\n" );
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document.write( "when x = 91, the first equation becomes 65 * t = 91\r<BR>\n" );
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document.write( "solve for t to get t = 91 / 65 = 1.4\r<BR>\n" );
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document.write( "when x = 91, the second equation becomes 75 * t = 196 - 91\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "75 * t = 105\r<BR>\n" );
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document.write( "solve for t to get t = 105 / 75 = 1.4\r<BR>\n" );
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document.write( "the time each traveled is the same, as it should be.\r<BR>\n" );
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document.write( "the first motorcyclist traveled 91 miles.\r<BR>\n" );
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document.write( "the second motorcyclist traveled 105 miles.\r<BR>\n" );
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document.write( "they met when they both traveled 1.4 hours.\r<BR>\n" );
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document.write( "if you figured the time for both riders, they you must have had 1.4 hours for each.\r<BR>\n" );
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document.write( "the actual time that they met could be anything, depending on when they both started.\r<BR>\n" );
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document.write( "1.4 hours is equal to 1 hour and 24 minutes.\r<BR>\n" );
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document.write( "if they both started at 10:00 am, they they met at 11:24 am.\r<BR>\n" );
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document.write( "if you looking for the number of miles that each traveled when they met, that would be 91 miles for the first rider and 105 miles for the second rider.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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