document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=715206>Question 715206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. I continually have difficulty solving distance problems involving multiple variables. Here is my question. Thank you so much.\r<BR>\n" );
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document.write( " A railroad and a highway intersect at right angles. A train is 10 miles from the intersection at the same moment that a car is 6 miles from the intersection. Both are traveling at 30 mph. How long until they are 4 miles apart?\r<BR>\n" );
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document.write( "There are two answers:<BR>\n" );
document.write( "First time = _______ minutes<BR>\n" );
document.write( "Second time = ______ minutes </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #439294 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=439294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A railroad and a highway intersect at right angles. A train is 10 miles from the intersection at the same moment that a car is 6 miles from the intersection. Both are traveling at 30 mph. How long until they are 4 miles apart? <BR>\n" );
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document.write( "Draw the picture so you can see what is happening with the distances:<BR>\n" );
document.write( "Train DATA:<BR>\n" );
document.write( "rate = 30 mph ; time = t hours ; distance = 30t miles<BR>\n" );
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document.write( "Car DATA:<BR>\n" );
document.write( "rate = 30 mph ; time = t hour ; distance = 30t miles<BR>\n" );
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document.write( "Distance train is from the intersection: 10-30t miles<BR>\n" );
document.write( "Distance car is from the intersection: 6-30t miles<BR>\n" );
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document.write( "Use Pythagoras:<BR>\n" );
document.write( "(10-30t)^2 + (6-30t)^2 = 4^2<BR>\n" );
document.write( "100 - 600t + 900t^2 + 36 - 360t + 900t^2 = 16<BR>\n" );
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document.write( "1800t^2 -960t + 120 = 0<BR>\n" );
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document.write( "Divide thru by 120 to get:<BR>\n" );
document.write( "15t^2 - 8t + 1 = 0<BR>\n" );
document.write( "(3t-1)(5t-1) = 0<BR>\n" );
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document.write( "t = 1/3 hr = 20 min<BR>\n" );
document.write( "Or<BR>\n" );
document.write( "t = 1/5 hr = 12 min <BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "==================== </SPAN>\n" );
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