document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118466>Question 1118466</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bus averages 6 miles per hour faster than a trolley. If the bus travels 90 miles in the same time it takes the trolley to travel 75 miles, then what is 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 #733783 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=733783\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time= distance.\r<BR>\n" );
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document.write( "let the rate of the trolley be equal to x.\r<BR>\n" );
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document.write( "the rate of the bus is then x + 6.\r<BR>\n" );
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document.write( "the bus travels 90 miles in the same time it takes the trolley to travel 75 miles.\r<BR>\n" );
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document.write( "what is the speed of each?\r<BR>\n" );
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document.write( "let T equal the time for each.\r<BR>\n" );
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document.write( "for the bus, the equation becomes (x + 6) * T = 90\r<BR>\n" );
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document.write( "for the trolley, the equation becomes x * T = 75\r<BR>\n" );
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document.write( "for the bus, the equation becomes x * T + 6 * T = 90\r<BR>\n" );
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document.write( "since x * T = 75 from the trolley equation, replace x * T in the bus equation with 75 to get 75 + 6 * T = 90\r<BR>\n" );
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document.write( "subtract 75 from both sides of the equation to get 6 * T = 90 - 75.\r<BR>\n" );
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document.write( "this becomes 6 * T = 15.\r<BR>\n" );
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document.write( "solve for T to get T = 2.5.\r<BR>\n" );
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document.write( "when T = 2.5 hours, the bus equation of (x + 6) * T = 90 becomes (x + 6) * 2.5 = 90.\r<BR>\n" );
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document.write( "this becomes 2.5 * x + 2.5 * 6 = 90 which becomes 2.5 * x + 15 = 90.\r<BR>\n" );
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document.write( "subtract 15 from both sides of this equation to get 2.5 * x = 75.\r<BR>\n" );
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document.write( "divide both sides of this equation by 2.5 to get x  30.\r<BR>\n" );
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document.write( "that's the speed of the trolley.\r<BR>\n" );
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document.write( "the speed of the bus is 30 + 6 = 36 miles per hours.\r<BR>\n" );
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document.write( "the time is 2.5 hours.<BR>\n" );
document.write( "the speed of the bus is 36 miles per hour.<BR>\n" );
document.write( "in 2.5 hours, the bus travels 36 * 2.5 = 90 miles.\r<BR>\n" );
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document.write( "the time is 2.5 hours.<BR>\n" );
document.write( "the speed of the trolley is 30 miles per hour.<BR>\n" );
document.write( "in 2.5 hours, the trolley travels 30 * 2.5 = 75 miles.\r<BR>\n" );
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document.write( "solution looks good.\r<BR>\n" );
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document.write( "solution is the speed of the bus is 36 miles per hours and the speed of the trolley is 30 miles per hour.\r<BR>\n" );
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document.write( "this could also have been solved a different way.\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "for the bus, the equation becomes (x + 6) * T = 90\r<BR>\n" );
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document.write( "for the trolley, the equation becomes x * T = 75\r<BR>\n" );
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document.write( "solve for T in each equation to get:\r<BR>\n" );
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document.write( "for the bus, T = 90 / (x + 6)\r<BR>\n" );
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document.write( "for the trolley, T = 75 / x\r<BR>\n" );
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document.write( "subtract the trolley equation from the bus equation to get:\r<BR>\n" );
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document.write( "0 = 90 / (x + 6) - 75 / x\r<BR>\n" );
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document.write( "multiply both sides of the equation by x to get:\r<BR>\n" );
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document.write( "0 = 90 * x / (x + 6) - 75\r<BR>\n" );
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document.write( "multiply both sides of the equation by (x + 6) to get:\r<BR>\n" );
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document.write( "0 = 90 * x - 75 * (x + 6)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "0 = 90 * x - 75 * x - 75 * 6\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "0 = 15 * x - 75 * 6\r<BR>\n" );
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document.write( "add 75 * 6 to both sides of the equation to get:\r<BR>\n" );
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document.write( "75 * 6 = 15 * x\r<BR>\n" );
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document.write( "divide both sides of the equation by 25 to get:\r<BR>\n" );
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document.write( "5 * 6 = x\r<BR>\n" );
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document.write( "solve for x to get x = 30\r<BR>\n" );
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document.write( "that's the speed of the trolley.\r<BR>\n" );
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document.write( "the speed of the bus is 6 more to get the speed of the bus = 36 miles per hour.\r<BR>\n" );
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document.write( "same solution, only achieved using a different method.\r<BR>\n" );
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document.write( "this second method did not require you to solve for T because T canceled out of the system of equations when you subtracted one equation from the other.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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