document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258233>Question 258233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two cars drive the 120 miles from town A to town B. The first car goes 10 mph faster than the second, and completes the journey in 1 hour less time. Let s be the speed of the slower car.<BR>\n" );
document.write( "(A) In terms of s, what is the speed of the faster car?<BR>\n" );
document.write( "(B) In terms of S, how long does the slower car take to complete the trip?<BR>\n" );
document.write( "(C) In terms of S, how long does the faster car take to complete the trip?<BR>\n" );
document.write( "(D) Express the conditions \"the faster car completes the journey in one hour less than the slower car\" as an equation involving s using the answers to part b and c.<BR>\n" );
document.write( "(E) Solve the equation in part d to find the speed of the slower car. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #190178 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=190178\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (A) In terms of s, what is the speed of the faster car?\r<BR>\n" );
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document.write( "faster car travels at s + 10 miles per hour.\r<BR>\n" );
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document.write( "(B) In terms of S, how long does the slower car take to complete the trip?\r<BR>\n" );
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document.write( "rate * time = distance.\r<BR>\n" );
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document.write( "this makes time = distance / rate.\r<BR>\n" );
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document.write( "slower car takes (120/s) hours to complete the trip.\r<BR>\n" );
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document.write( "(C) In terms of s, how long does the faster car take to complete the trip?\r<BR>\n" );
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document.write( "faster car takes (120 / (s+10)) hours to complete the trip.\r<BR>\n" );
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document.write( "(D) Express the conditions \"the faster car completes the journey in one hour less than the slower car\" as an equation involving s using the answers to part b and c.\r<BR>\n" );
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document.write( "the time it takes the slower car is expressed by the equation:\r<BR>\n" );
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document.write( "h[s] = 120/s where h represents the time in hours.\r<BR>\n" );
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document.write( "the time it takes the faster car is expressed by the equation:\r<BR>\n" );
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document.write( "h[f] = 120/(s+10) where h represents the time in hours.\r<BR>\n" );
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document.write( "the statement that it takes the faster car one less hour to complete the trip can be expressed by the equation h[f] = h[s] - 1.\r<BR>\n" );
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document.write( "replace h[f] and h[s] with their respective equivalents and you get:\r<BR>\n" );
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document.write( "120/(s+10) = 120/s - 1\r<BR>\n" );
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document.write( "(E) Solve the equation in part d to find the speed of the slower car.\r<BR>\n" );
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document.write( "the equation in part D is:\r<BR>\n" );
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document.write( "120/(s+10) = 120/s - 1\r<BR>\n" );
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document.write( "multiply both sides of this equation by s * (s+10) to get:\r<BR>\n" );
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document.write( "120 * s = 120 * (s+10) - (1 * (s+10) * s)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "120 * s = 120 * s + 1200 - (s^2 + 10*s))\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "120 * s = 120 * s + 1200 - s^2 - 10*s\r<BR>\n" );
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document.write( "subtract 120 * s from both sides of this equation to get:\r<BR>\n" );
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document.write( "0 = 120 * s - 120 * s + 1200 - s^2 - 10*s\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "0 = 1200 - s^2 - 10*s\r<BR>\n" );
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document.write( "add s^2 to both sides of this equation and add 10*s to both sides of this equation and subtract 1200 from both sides of this equation to get:\r<BR>\n" );
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document.write( "s^2 + 10*s - 1200 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get:\r<BR>\n" );
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document.write( "(s+40) * (s-30) = 0\r<BR>\n" );
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document.write( "solve for s to get s = -40 or s = 30\r<BR>\n" );
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document.write( "since s can't be negative, then s must equal 30.\r<BR>\n" );
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document.write( "speed of the slower car is 30 miles per hour.\r<BR>\n" );
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document.write( "speed of the faster car is 40 miles per hour.\r<BR>\n" );
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document.write( "since time = distance / rate, then:\r<BR>\n" );
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document.write( "the time it takes the slower car = 120/30 = 4 hours.\r<BR>\n" );
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document.write( "the time it takes the faster car = 120/40 = 3 hours.\r<BR>\n" );
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document.write( "the faster car takes 1 hour less than the slower car so the equation is satisfied.\r<BR>\n" );
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document.write( "answer to part E is that the speed of the slower car is 30 miles per hour.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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