document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80682>Question 80682</A>: <I><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.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57837 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=57837\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For this equation you use the formula:<BR>\n" );
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document.write( "D = R*T<BR>\n" );
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document.write( "where D = the distance traveled, R = the rate or speed, and T = the time<BR>\n" );
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document.write( "The rate and the time are the two unknowns. For the 200 miles we can write the equation for <BR>\n" );
document.write( "the actual trip as:<BR>\n" );
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document.write( "200 = R * T     <--- call this the first equation<BR>\n" );
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document.write( "For the proposed trip you know that the new rate equals the old rate plus 10 mph. You can<BR>\n" );
document.write( "write this new rate as (R + 10).<BR>\n" );
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document.write( "And you also know that the new time is an hour less than the old time. You can write this<BR>\n" );
document.write( "new time as (T - 1)<BR>\n" );
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document.write( "Therefore you can write the equation for the new trip as:<BR>\n" );
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document.write( "200 = (R + 10)*(T - 1)<BR>\n" );
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document.write( "Multiply the right side out to get:<BR>\n" );
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document.write( "200 = R*T - R + 10*T - 10   <--- call this the second equation<BR>\n" );
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document.write( "Since you need to solve this second equation for R, solve the first equation for T in terms of<BR>\n" );
document.write( "R and then substitute that into this second equation.<BR>\n" );
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document.write( "Solving the first equation for T in terms of R you divide both sides by R and you get:<BR>\n" );
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document.write( "200 = T * R<BR>\n" );
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document.write( "200/R = (T*R)/R<BR>\n" );
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document.write( "200/R = T<BR>\n" );
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document.write( "Now substitute the left side of this equation into the second equation to get:<BR>\n" );
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document.write( "200 = R*(200/R) - R + 10*(200/R) - 10<BR>\n" );
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document.write( "Simplify this by multiplying out the right side:<BR>\n" );
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document.write( "200 = 200 - R + (2000/R) - 10<BR>\n" );
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document.write( "Subtract 200 from both sides and the equation becomes:<BR>\n" );
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document.write( "0 = - R + 2000/R - 10<BR>\n" );
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document.write( "Multiply both sides by -R and you get:<BR>\n" );
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document.write( "0 = R^2 - 2000R/R + 10R<BR>\n" );
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document.write( "The middle term on the right side simplifies to -2000 and the equation becomes:<BR>\n" );
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document.write( "0 = R^2 - 2000 + 10R<BR>\n" );
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document.write( "Transpose this equation (switch sides) and rearrange terms so it is in the more conventional<BR>\n" );
document.write( "form of:<BR>\n" );
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document.write( "R^2 + 10R - 2000 = 0<BR>\n" );
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document.write( "This equation factors into:<BR>\n" );
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document.write( "(R + 50)*(R - 40) = 0<BR>\n" );
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document.write( "This equation will be true if either factor on the left side equals zero. So set each equal<BR>\n" );
document.write( "to zero and solve for R:<BR>\n" );
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document.write( "R + 50 = 0<BR>\n" );
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document.write( "Subtract 50 from both sides and R becomes:<BR>\n" );
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document.write( "R = -50 mph<BR>\n" );
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document.write( "Then set the second factor equal to zero:<BR>\n" );
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document.write( "R - 40 = 0<BR>\n" );
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document.write( "Add 40 to both sides to get:<BR>\n" );
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document.write( "R = 40 mph<BR>\n" );
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document.write( "Ignore the first answer of -50 mph because a negative speed doesn't really make sense.<BR>\n" );
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document.write( "So the answer is 40 mph as the speed.<BR>\n" );
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document.write( "Check this out. At 40 mph you drive the 200 miles in 5 hours.<BR>\n" );
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document.write( "Now increase the speed by 10 mph to 50 mph.  If you drive 200 miles at 50 mph it will<BR>\n" );
document.write( "take 4 hours.  The answer checks ... increasing the speed to 50 mph reduces the time it<BR>\n" );
document.write( "takes to drive 200 miles by 1 hour.<BR>\n" );
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document.write( "So the answer to the original rate is 40 mph.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and a way that you can solve it.<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( " </SPAN>\n" );
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