document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011876>Question 1011876</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person is travelling by train and car in his whole journey.. The matter is if he is travelling first by train till 60 kms and the rest by car, then his total journey has taken 4 hours.. but if he is travelling first by train till 100 kms, then his journey has taken 10 mins more than before.. According to the question, what was the speed of that train?? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627683 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39621)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=627683\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two arrangements of travel are described.  The individual time quantities are not given but overall time quantities are given.  Descriptions of rates are not given.  Let d be the trip's distance.\r<BR>\n" );
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document.write( "Arrangement A\r\n" );
document.write( "                 rate    time    distance\r\n" );
document.write( "TRAIN             R              60\r\n" );
document.write( "CAR               r              d-60\r\n" );
document.write( "Total                    4\r\n" );
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document.write( "Arrangement B\r\n" );
document.write( "                rate     time     distance\r\n" );
document.write( "TRAIN            R                 100\r\n" );
document.write( "CAR              r                 d-100\r\n" );
document.write( "Total                    4&1/6\r\n" );
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document.write( "Fill the missing time slots according to y=mx, x=y/m.\r<BR>\n" );
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document.write( "Arrangement A\r\n" );
document.write( "                 rate    time        distance\r\n" );
document.write( "TRAIN             R      60/R        60\r\n" );
document.write( "CAR               r      (d-60)/r    d-60\r\n" );
document.write( "Total                    4\r\n" );
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document.write( "Arrangement B\r\n" );
document.write( "                rate     time        distance\r\n" );
document.write( "TRAIN            R       100/R        100\r\n" );
document.write( "CAR              r       (d-100)/r    d-100\r\n" );
document.write( "Total                    4&1/6\r\n" );
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document.write( "Note that 10 minutes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > of an hour.\r<BR>\n" );
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document.write( "You have two time-sum equations to make.  The system of equations is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2860%2FR%2B%28d-60%29%2Fr=4%2C100%2FR%2B%28d-100%29%2Fr=4%261%2F6%29 ALIGN=MIDDLE  ALT=\"system%2860%2FR%2B%28d-60%29%2Fr=4%2C100%2FR%2B%28d-100%29%2Fr=4%261%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Do you see ANYTHING else?<BR>\n" );
document.write( "<i>MAYBE</i> the time difference of the two arrangements?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2FR%2B%28d-60%29%2Fr%2B1%2F6=100%2FR%2B%28d-100%29%2Fr ALIGN=MIDDLE  ALT=\"60%2FR%2B%28d-60%29%2Fr%2B1%2F6=100%2FR%2B%28d-100%29%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A few steps of work on this time difference equation gives simplified <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2FR-40%2Fr=1%2F6 ALIGN=MIDDLE  ALT=\"40%2FR-40%2Fr=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Return now to the system of two equations with the three variables, r, R, d, and solve each of them for d; and then equate the expressions!  I will not include showing those steps here, but you may get an equation consistent with  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2F6-100r%2FR%2B60r%2FR=0 ALIGN=MIDDLE  ALT=\"r%2F6-100r%2FR%2B60r%2FR=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2F6-40r%2FR=0 ALIGN=MIDDLE  ALT=\"r%2F6-40r%2FR=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You have from this another system of two equations in just r and R:<BR>\n" );
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document.write( "I did not try to solve this further. </SPAN>\n" );
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