document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205745>Question 1205745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Trashia left Riverside, California, driving her motorhome north on Interstate 15 towards Salt Lake City at a speed of 40 miles per hour. Half an hour later, Karissa left Riverside in her car on the same route as Trashia, driving 60 miles per hour. Solve the system:\r<BR>\n" );
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document.write( "{(40 y=60 x),(y=x+1/2) :}\r<BR>\n" );
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document.write( "A. for x to find out how long it will take Karissa to<BR>\n" );
document.write( "catch up to Trashia.\r<BR>\n" );
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document.write( "B. What is the value of y the number of hours<BR>\n" );
document.write( "Trashia will have driven before Karissa catches up<BR>\n" );
document.write( "to her?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842750 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=842750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your two equations that you show that need to be solved simultaneously are:\r<BR>\n" );
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document.write( "40y = 60x<BR>\n" );
document.write( "y = x + 1/2\r<BR>\n" );
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document.write( "in the first equation, replace y with x + 1/2 from the second equation to get:\r<BR>\n" );
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document.write( "40 * (x + 1/2) = 60 * x<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "40 * x + 40 * 1/2 = 60 * x<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "40 * x + 20 = 60 * x<BR>\n" );
document.write( "subtract 40 * x from both sides of the equation to get:<BR>\n" );
document.write( "20 = 60 * x - 40 * x<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "20 = 20 * x<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 1\r<BR>\n" );
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document.write( "go back to your original two equations and replace x with 1.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "40y = 60x becomes 40y = 60 * 1<BR>\n" );
document.write( "simplify to get 40y = 60<BR>\n" );
document.write( "divide both sides of the equation by 40 to get:<BR>\n" );
document.write( "y = 60/40 = 1.5\r<BR>\n" );
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document.write( "y = x + 1/2<BR>\n" );
document.write( "replace x with 1 to get:<BR>\n" );
document.write( "y = 1 + 1/2<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "y = 1.5.\r<BR>\n" );
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document.write( "both equations get y = 1.5\r<BR>\n" );
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document.write( "your solution is x = 1 and y = 1.5\r<BR>\n" );
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document.write( "answers to your questions are:\r<BR>\n" );
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document.write( "A. for x to find out how long it will take Karissa to<BR>\n" );
document.write( "catch up to Trashia.\r<BR>\n" );
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document.write( "trashia was traveling at 40 miles per hour.<BR>\n" );
document.write( "karissa was traveling at 60 miles per hour.\r<BR>\n" );
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document.write( "y is the time that trashia was driving.<BR>\n" );
document.write( "x is the time that karissa was driving.\r<BR>\n" );
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document.write( "since y = 1.5, then trashia was traveling for 1.5 hours at 40 miles per hour for a distance of 60 miles.\r<BR>\n" );
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document.write( "since x = 1, then karissa was traveling for 1 hour at 60 miles per hour for a distance of 60 miles.\r<BR>\n" );
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document.write( "karissa caught up to trashia at the 60 mile mark.\r<BR>\n" );
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document.write( "it took karissa 1 hour to catch up to trashia.\r<BR>\n" );
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document.write( "B. What is the value of y the number of hours<BR>\n" );
document.write( "Trashia will have driven before Karissa catches up<BR>\n" );
document.write( "to her?\r<BR>\n" );
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document.write( "y is equal to 1.5 hours.<BR>\n" );
document.write( "x is equal to 1 hour.\r<BR>\n" );
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document.write( "trashia was driving for 1.5 hours before karissa caught up to her.\r<BR>\n" );
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document.write( "i usually solve problems like these as follows:\r<BR>\n" );
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document.write( "the basic formula is rate * time = distance.\r<BR>\n" );
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document.write( "for trashia, the formula becomes 40 * y = d<BR>\n" );
document.write( "40 is the rate, y is the time, d is the distance.\r<BR>\n" );
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document.write( "for karissa, the formula becomes 60 * x = d<BR>\n" );
document.write( "60 is the rate, x is the tie, d is the distance.\r<BR>\n" );
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document.write( "you are then given tht y = x + 1/2.\\r<BR>\n" );
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document.write( "the two formulas become:<BR>\n" );
document.write( "40 * (x + 1/2) = d<BR>\n" );
document.write( "60 * x = d\r<BR>\n" );
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document.write( "since they are both equal to d, you can set the expressions on the left side of each equation equal to each other to get:\r<BR>\n" );
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document.write( "40 * (x + 1/2) = 60 * x<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "40 * x + 20 = 60 * x<BR>\n" );
document.write( "subtract 40 * x from both sides of the equation to get:<BR>\n" );
document.write( "20 = 20 * x<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 1<BR>\n" );
document.write( "since y = x + 1/2, you get y = 1.5\r<BR>\n" );
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document.write( "i only mentioned all this to let you know that you were dealing with a basic rate * time = distance type formula.\r<BR>\n" );
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document.write( "if you find that informative, fine.<BR>\n" );
document.write( "if not, distregard.\r<BR>\n" );
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document.write( "any additional questions or concerns regarding this problem can be addressed to me.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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