document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198257>Question 198257</A>: <I><SPAN STYLE=\"word-break: break-all;\"> respected sir,\r<BR>\n" );
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document.write( "1] A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10 th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30 th of a minute. What is B’s speed in m/s?\r<BR>\n" );
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document.write( "plz solve my doubt..\r<BR>\n" );
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document.write( "thank u. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148746 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=148746\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What the problem doesn't say, and must be assumed is that<BR>\n" );
document.write( "A and B each travel at constant speeds. I can then write a<BR>\n" );
document.write( "constant speed equation for each and for each race:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Ba%5D+=+r%5Ba%5D%2At%5Ba%5D ALIGN=MIDDLE  ALT=\"d%5Ba%5D+=+r%5Ba%5D%2At%5Ba%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D ALIGN=MIDDLE  ALT=\"d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If a have a stopwatch, I want to start timing the race when<BR>\n" );
document.write( "both runners are in motion, so I'll start it when A begins<BR>\n" );
document.write( "running for each race.<BR>\n" );
document.write( "1st race:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Ba%5D+=+480 ALIGN=MIDDLE  ALT=\"d%5Ba%5D+=+480\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bb%5D+=+480+-+48 ALIGN=MIDDLE  ALT=\"d%5Bb%5D+=+480+-+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bb%5D+=+432 ALIGN=MIDDLE  ALT=\"d%5Bb%5D+=+432\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Ba%5D+=+t%5Bb%5D+-+1%2F10 ALIGN=MIDDLE  ALT=\"t%5Ba%5D+=+t%5Bb%5D+-+1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bb%5D+=+t%5Ba%5D+%2B+1%2F10 ALIGN=MIDDLE  ALT=\"t%5Bb%5D+=+t%5Ba%5D+%2B+1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480+=+r%5Ba%5D%2At%5Ba%5D ALIGN=MIDDLE  ALT=\"480+=+r%5Ba%5D%2At%5Ba%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > (same for both races)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432+=+r%5Bb%5D%2A%28t%5Ba%5D+%2B+1%2F10%29 ALIGN=MIDDLE  ALT=\"432+=+r%5Bb%5D%2A%28t%5Ba%5D+%2B+1%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "2nd race:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Ba%5D+=+480 ALIGN=MIDDLE  ALT=\"d%5Ba%5D+=+480\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bb%5D+=+480+-+144 ALIGN=MIDDLE  ALT=\"d%5Bb%5D+=+480+-+144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bb%5D+=+336 ALIGN=MIDDLE  ALT=\"d%5Bb%5D+=+336\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bb%5D+=+t%5Ba%5D+-+1%2F30 ALIGN=MIDDLE  ALT=\"t%5Bb%5D+=+t%5Ba%5D+-+1%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480+=+r%5Ba%5D%2At%5Ba%5D ALIGN=MIDDLE  ALT=\"480+=+r%5Ba%5D%2At%5Ba%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=336+=+r%5Bb%5D%2A%28t%5Ba%5D+-+1%2F30%29 ALIGN=MIDDLE  ALT=\"336+=+r%5Bb%5D%2A%28t%5Ba%5D+-+1%2F30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "r[a] and r[b] are the same in both races.<BR>\n" );
document.write( "Also, t[a] is the same in both races, but<BR>\n" );
document.write( "t[b] is not the same .<BR>\n" );
document.write( "In race 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432+=+r%5Bb%5D%2A%28t%5Ba%5D+%2B+1%2F10%29 ALIGN=MIDDLE  ALT=\"432+=+r%5Bb%5D%2A%28t%5Ba%5D+%2B+1%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bb%5D+=+432%2F%28t%5Ba%5D+%2B+1%2F10%29 ALIGN=MIDDLE  ALT=\"r%5Bb%5D+=+432%2F%28t%5Ba%5D+%2B+1%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can plug this into the equation from race 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=336+=+r%5Bb%5D%2A%28t%5Ba%5D+-+1%2F30%29 ALIGN=MIDDLE  ALT=\"336+=+r%5Bb%5D%2A%28t%5Ba%5D+-+1%2F30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=336+=+%28432%2F%28t%5Ba%5D+%2B+1%2F10%29%29%2A%28t%5Ba%5D+-+1%2F30%29 ALIGN=MIDDLE  ALT=\"336+=+%28432%2F%28t%5Ba%5D+%2B+1%2F10%29%29%2A%28t%5Ba%5D+-+1%2F30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Ba%5D+%2B+1%2F10 ALIGN=MIDDLE  ALT=\"t%5Ba%5D+%2B+1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=336%2A%28t%5Ba%5D+%2B+1%2F10%29+=+432%2A%28t%5Ba%5D+-+1%2F30%29 ALIGN=MIDDLE  ALT=\"336%2A%28t%5Ba%5D+%2B+1%2F10%29+=+432%2A%28t%5Ba%5D+-+1%2F30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=336t%5Ba%5D+%2B+33.6+=+432t%5Ba%5D+-+14.4 ALIGN=MIDDLE  ALT=\"336t%5Ba%5D+%2B+33.6+=+432t%5Ba%5D+-+14.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96t%5Ba%5D+=+48 ALIGN=MIDDLE  ALT=\"96t%5Ba%5D+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Ba%5D+=+.5 ALIGN=MIDDLE  ALT=\"t%5Ba%5D+=+.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The time for A is 30 sec<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480+=+r%5Ba%5D%2At%5Ba%5D ALIGN=MIDDLE  ALT=\"480+=+r%5Ba%5D%2At%5Ba%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480+=+r%5Ba%5D%2A.5 ALIGN=MIDDLE  ALT=\"480+=+r%5Ba%5D%2A.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Ba%5D+=+960 ALIGN=MIDDLE  ALT=\"r%5Ba%5D+=+960\"   DISABLED_style= \"max-width:90%; height:auto;\" > m/min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432+=+r%5Bb%5D%2A%28t%5Ba%5D+%2B+1%2F10%29 ALIGN=MIDDLE  ALT=\"432+=+r%5Bb%5D%2A%28t%5Ba%5D+%2B+1%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (1st race)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432+=+r%5Bb%5D%2A%28.5+%2B+.1%29 ALIGN=MIDDLE  ALT=\"432+=+r%5Bb%5D%2A%28.5+%2B+.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bb%5D+=+432%2F.6 ALIGN=MIDDLE  ALT=\"r%5Bb%5D+=+432%2F.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bb%5D+=+720 ALIGN=MIDDLE  ALT=\"r%5Bb%5D+=+720\"   DISABLED_style= \"max-width:90%; height:auto;\" > m/min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720 ALIGN=MIDDLE  ALT=\"720\"   DISABLED_style= \"max-width:90%; height:auto;\" > m/min * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F60 ALIGN=MIDDLE  ALT=\"1%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > min/sec = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > m/sec<BR>\n" );
document.write( "B's speed is 12 m/sec<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=336+=+r%5Bb%5D%2A%28t%5Ba%5D+-+1%2F30%29 ALIGN=MIDDLE  ALT=\"336+=+r%5Bb%5D%2A%28t%5Ba%5D+-+1%2F30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (2nd race)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=336+=+r%5Bb%5D%2A%2815%2F30+-+1%2F30%29 ALIGN=MIDDLE  ALT=\"336+=+r%5Bb%5D%2A%2815%2F30+-+1%2F30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=336+=+r%5Bb%5D%2A%2814%2F30%29 ALIGN=MIDDLE  ALT=\"336+=+r%5Bb%5D%2A%2814%2F30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bb%5D+=+10080%2F14 ALIGN=MIDDLE  ALT=\"r%5Bb%5D+=+10080%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bb%5D+=+720 ALIGN=MIDDLE  ALT=\"r%5Bb%5D+=+720\"   DISABLED_style= \"max-width:90%; height:auto;\" > m/min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720 ALIGN=MIDDLE  ALT=\"720\"   DISABLED_style= \"max-width:90%; height:auto;\" > m/min = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > m/sec<BR>\n" );
document.write( "OK<BR>\n" );
document.write( "To see the whole thing, I could plot time (sec) on<BR>\n" );
document.write( "the x-axis and distance (m) on the y-axis for<BR>\n" );
document.write( "I want to look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+480 ALIGN=MIDDLE  ALT=\"d+=+480\"   DISABLED_style= \"max-width:90%; height:auto;\" >m<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+16t ALIGN=MIDDLE  ALT=\"d+=+16t\"   DISABLED_style= \"max-width:90%; height:auto;\" > (both races)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+-+48+=+12t ALIGN=MIDDLE  ALT=\"d+-+48+=+12t\"   DISABLED_style= \"max-width:90%; height:auto;\" > B, 1st race<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+-+144+=+12t ALIGN=MIDDLE  ALT=\"d+-+144+=+12t\"   DISABLED_style= \"max-width:90%; height:auto;\" > B, 2nd race<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+700%2C+400%2C+-10%2C+60%2C+-50%2C+700%2C+16x%2C12x+%2B+48%2C12x+%2B+144%29+ ALIGN=MIDDLE  ALT=\"+graph%28+700%2C+400%2C+-10%2C+60%2C+-50%2C+700%2C+16x%2C12x+%2B+48%2C12x+%2B+144%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The line starting at the origin is A's plot.<BR>\n" );
document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+480 ALIGN=MIDDLE  ALT=\"d+=+480\"   DISABLED_style= \"max-width:90%; height:auto;\" > shows the times to get to finish<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+700%2C+400%2C+-10%2C+60%2C+300%2C+700%2C+16x%2C12x+%2B+48%2C12x+%2B+144%29+ ALIGN=MIDDLE  ALT=\"+graph%28+700%2C+400%2C+-10%2C+60%2C+300%2C+700%2C+16x%2C12x+%2B+48%2C12x+%2B+144%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a blow-up    </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );