document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127370>Question 127370</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two trains are 276 miles apart, and their speeds differ by 10mph. they are traveling towards each other and will meet in 3 hours. find the speed of the slower train </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93329 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=93329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start by letting x represent the speed of one of the trains and y represent the speed of the<BR>\n" );
document.write( "other. The problem tells you that the two trains have speeds that are different by 10 mph.<BR>\n" );
document.write( "In other words, if you subtract the two speeds, the answer will be 10 mph. In equation form<BR>\n" );
document.write( "this is:<BR>\n" );
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document.write( "x - y = 10<BR>\n" );
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document.write( "This is the first equation that we need.<BR>\n" );
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document.write( "Next we use the distance formula. The distance a train travels is equal to the speed of<BR>\n" );
document.write( "the train times the amount of time the train travels at that speed. Note that the trains each<BR>\n" );
document.write( "travel for 3 hours. Therefore, the distance each travels during that time is its speed times 3.<BR>\n" );
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document.write( "So the distance one train travels is x times 3 and the distance the other train travels is<BR>\n" );
document.write( "y times 3. If you total these two distances they must add up to be 276 miles, the distance<BR>\n" );
document.write( "between them before they meet. In equation form this is:<BR>\n" );
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document.write( "3x + 3y = 276<BR>\n" );
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document.write( "This is the second equation we need. <BR>\n" );
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document.write( "Now return to the first equation, and let's solve for one of the unknown speeds in terms of<BR>\n" );
document.write( "the other. For example we can solve for x by adding y to both sides of the equation. On<BR>\n" );
document.write( "the left side the -y cancels the y we are adding and on the right side the y we are adding<BR>\n" );
document.write( "appears. So, when we add y to both sides of the first equation, that equation is transformed<BR>\n" );
document.write( "to:<BR>\n" );
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document.write( "x = 10 + y<BR>\n" );
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document.write( "Since x and 10 + y are equal, we can go to the second equation and substitute 10 + y for x<BR>\n" );
document.write( "and then the second equation becomes:<BR>\n" );
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document.write( "3*(10 + y) + 3y = 276<BR>\n" );
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document.write( "Multiply out the left side by multiplying 3 times each of the terms in the parentheses<BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "30 + 3y + 3y = 276<BR>\n" );
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document.write( "Add together the two terms that contain y and the sum is 6y. This makes the equation<BR>\n" );
document.write( "become:<BR>\n" );
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document.write( "30 + 6y = 276<BR>\n" );
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document.write( "Get rid of the 30 on the left side by subtracting 30 from both sides. When you take away<BR>\n" );
document.write( "30 from both sides the equation is reduced to:<BR>\n" );
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document.write( "6y = 246<BR>\n" );
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document.write( "Solve for y by dividing both sides of this equation by 6 since 6 is the multiplier <BR>\n" );
document.write( "of y. Dividing both sides by 6 changes the equation to:<BR>\n" );
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document.write( "y = 246/6 = 41<BR>\n" );
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document.write( "Now we know that the speed of one train is 41 mph. We can find the speed of the second train<BR>\n" );
document.write( "by substituting 41 for y in either of the two original equations and then solving the<BR>\n" );
document.write( "resulting equation for x. The easier equation to use in this case is the first equation in<BR>\n" );
document.write( "which we had:<BR>\n" );
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document.write( "x - y = 10<BR>\n" );
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document.write( "Substitute 41 for y and this becomes:<BR>\n" );
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document.write( "x - 41 = 10<BR>\n" );
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document.write( "Solve for x by adding 41 to both sides. On the left side the -41 is canceled out by the added 41.<BR>\n" );
document.write( "On the right side you have 10 + 41 and the resulting equation is<BR>\n" );
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document.write( "x = 51 <BR>\n" );
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document.write( "So the other train is going at 51 mph<BR>\n" );
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document.write( "Check the answers. Is there 10 mph difference in their speeds? Sure is. Then at 51 mph<BR>\n" );
document.write( "for 3 hours one of the trains goes 3*51 = 153 miles. And at 41 mph for 3 hours the other<BR>\n" );
document.write( "train goes 3*41 = 123 miles. So the total distance the trains travel is 153 +123 = 276 miles,<BR>\n" );
document.write( "the distance they had to go before they meet. This checks also, so our two answers are<BR>\n" );
document.write( "correct. One of the trains is going at 51 mph and the other is going at 41 mph.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and a way that you can use to solve it.<BR>\n" );
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