document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206592>Question 206592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I know rate times time equals distance, but I'm still confused. Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156129 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=156129\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle. <BR>\n" );
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document.write( "let x = the certain speed in miles per hour.<BR>\n" );
document.write( "let h = the time it took in hours.<BR>\n" );
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document.write( "rate * time = distance becomes x * h = 200<BR>\n" );
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document.write( "if he had gone 10 mph faster his rate would have been 10 mph more than whaqt it was which is the same as x + 10<BR>\n" );
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document.write( "if he had gone 10 mph faster his time would have been 1 hour less which is the same as h - 1<BR>\n" );
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document.write( "solve for x<BR>\n" );
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document.write( "you have 2 equations.<BR>\n" );
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document.write( "the first equation is x * h = 200<BR>\n" );
document.write( "the second equation is (x+10)*(h-1) = 200<BR>\n" );
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document.write( "since both equations are equal to 200 then they are equal to each other.<BR>\n" );
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document.write( "your equation becomes:<BR>\n" );
document.write( "x*h = (x+10)*(h-1)<BR>\n" );
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document.write( "if you multiply this out you get h^2 - h - 20 = 0 which factors out to be (h-5) * (h+4) = 0 which makes h = 5 or h = -4.<BR>\n" );
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document.write( "since h = -4 is not possible your answer has to be be h = 5<BR>\n" );
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document.write( "if you substitute 5 for h in your first equation you get 5x = 200 which makes x = 40<BR>\n" );
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document.write( "your answer should be:<BR>\n" );
document.write( "x = 40 = speed he traveled at.<BR>\n" );
document.write( "h = 5 = number of hours it took.<BR>\n" );
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document.write( "5*40 = 200 so this part checks out.<BR>\n" );
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document.write( "second part states if he went 10 mph faster he would have taken 1 hour less.<BR>\n" );
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document.write( "10 mph faster would be 50 mph.<BR>\n" );
document.write( "1 hour less would be 4 hours.<BR>\n" );
document.write( "50 * 4 = 200 so this part checks out also.<BR>\n" );
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document.write( "answer is his original rate of travel was 40 miles per hour and the original time it took was 5 hours.<BR>\n" );
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