document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=336203>Question 336203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On a recent trip, Sarahs car traveled 20 mph faster on the first 200 miles that it did on the remaining 80 miles. The total time for the trip was 4 hours. Find the speed of Sarahs car on the first part of the trip.\r<BR>\n" );
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document.write( "a) 13 mph  b) 77 mph  c) 68 mph  d) 57 mph\r<BR>\n" );
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document.write( "I came up with b) 77 but was not sure if this was correct. Could you please show me the correct way to work this problem out. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #241093 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=241093\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> On a recent trip, Sarahs car traveled 20 mph faster on the first 200 miles that<BR>\n" );
document.write( " it did on the remaining 80 miles.<BR>\n" );
document.write( " The total time for the trip was 4 hours. Find the speed of Sarahs car on the first part of the trip.<BR>\n" );
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document.write( "Let s = speed on the 1st part of the trip (200 mi)<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-20) = speed on the last part (80 mi)<BR>\n" );
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document.write( "Write a time equation: time = dist/speed<BR>\n" );
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document.write( "Fast speed time + slow speed time = 4 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fs ALIGN=MIDDLE  ALT=\"200%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2F%28%28s-20%29%29 ALIGN=MIDDLE  ALT=\"80%2F%28%28s-20%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4<BR>\n" );
document.write( "multiply equation by s(s-20),results:<BR>\n" );
document.write( "200(s-20) + 80s = 4s(s-20)<BR>\n" );
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document.write( "200s - 4000 + 80s = 4s^2 - 80s<BR>\n" );
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document.write( "280s - 4000 = 4s^2 - 80s<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "0 = 4s^2 - 80s - 280s + 4000 <BR>\n" );
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document.write( "4s^2 - 360s + 4000 = 0<BR>\n" );
document.write( "simplify divide by 4<BR>\n" );
document.write( "s^2 - 90s + 1000 = 0<BR>\n" );
document.write( "Solving this with quadratic formula got two solutions: s=13 and s=77<BR>\n" );
document.write( "Obviously s = 77 mph is the one<BR>\n" );
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document.write( "Check it find the time at each speed<BR>\n" );
document.write( "200/77 = 2.6 hr<BR>\n" );
document.write( "80/57  = 1.4 hrs<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "total time 4 hrs </SPAN>\n" );
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