document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=638443>Question 638443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two contestants run a 440-yard course. The first wins by 4 seconds when given a head start of 200 feet. They finish together when the first is given a head start of 40 yards. Find the speed of each in feet per second. \r<BR>\n" );
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document.write( "I tried to solve by using the formula D (distance)= s (speed) x t (time). <BR>\n" );
document.write( "But I come up with two equations for each situation. Converting yards to feet: 440yards=1320 feet: <BR>\n" );
document.write( "runner #1: s(t-4)=1120   (wins by 4 seconds)<BR>\n" );
document.write( "runner #2: s(t)=1320     \r<BR>\n" );
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document.write( "and for the second situation:<BR>\n" );
document.write( "runner #1: s(t)=1200 (given a 40 yard=120feet head start:  1320-120=1200 feet). <BR>\n" );
document.write( "runner #2  s(t)=1320<BR>\n" );
document.write( "then solving for s: s=1320/t and substituting 1320/t(t-4)=1120 and solving for t, 1320t-5280=1120t, t=26.4 secs, then s=1320/t and s=1320/26.4= 50ft/sec. \r<BR>\n" );
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document.write( "Now, obviously a human cannot run at that speed, so this does not seem like a plausible answer, and I cannot figure out why I have four equations, I also tried to use different combinations but this didn't work either. So, I trust someone with better mathematical acumen can come up with a better solution. Thank you so kindly for trying to solve this problem. I look forward to the correct solution and appreciate your time and assistance.   \r<BR>\n" );
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document.write( "Two contestants run a 440-yard course. The first wins by 4 seconds when given a head start of 200 feet. They finish together when the first is given a head start of 40 yards. Find the speed of each in feet per second. \r<BR>\n" );
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document.write( "I tried to solve by using the formula D (distance)= s (speed) x t (time). <BR>\n" );
document.write( "But I come up with two equations for each situation. Converting yards to feet: 440yards=1320 feet: <BR>\n" );
document.write( "runner #1: s(t-4)=1120   (wins by 4 seconds)<BR>\n" );
document.write( "runner #2: s(t)=1320     \r<BR>\n" );
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document.write( "and for the second situation:<BR>\n" );
document.write( "runner #1: s(t)=1200 (given a 40 yard=120feet head start:  1320-120=1200 feet). <BR>\n" );
document.write( "runner #2  s(t)=1320<BR>\n" );
document.write( "then solving for s: s=1320/t and substituting 1320/t(t-4)=1120 and solving for t, 1320t-5280=1120t, t=26.4 secs, then s=1320/t and s=1320/26.4= 50ft/sec. \r<BR>\n" );
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document.write( "Now, obviously a human cannot run at that speed, so this does not seem like a plausible answer, and I cannot figure out why I have four equations, I also tried to use different combinations but this didn't work either. So, I trust someone with better mathematical acumen can come up with a better solution. Thank you so kindly for trying to solve this problem. I look forward to the correct solution and appreciate your time and assistance. \r<BR>\n" );
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document.write( "Let the speed of the 1st runner be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B1%5D ALIGN=MIDDLE  ALT=\"S%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and speed of 2nd, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B2%5D ALIGN=MIDDLE  ALT=\"S%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The course is 440 yards, or 1,320 feet<BR>\n" );
document.write( "Since the 1st gets a headstart of 200 feet, then the 1st travels 1,320 – 200, or 1,120 feet\r<BR>\n" );
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document.write( "Time taken by 1st to go 1,120 feet, plus time won by, equals time taken by 2nd to go 1,320 ft, OR\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1120%2FS%5B1%5D+%2B+4+=+1320%2FS%5B2%5D ALIGN=MIDDLE  ALT=\"1120%2FS%5B1%5D+%2B+4+=+1320%2FS%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1120S%5B2%5D+%2B+4S%5B1%5DS%5B2%5D+=+1320S%5B1%5D ALIGN=MIDDLE  ALT=\"1120S%5B2%5D+%2B+4S%5B1%5DS%5B2%5D+=+1320S%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- Multiplying by LCD, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B1%5DS%5B2%5D ALIGN=MIDDLE  ALT=\"S%5B1%5DS%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- eq (i)\r<BR>\n" );
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document.write( "Since the 1st gets a headstart of 40 yards, or 120 feet, then the 1st travels 1,320 – 120, or 1,200 feet\r<BR>\n" );
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document.write( "Time taken by 1st to go 1,200 feet equals time taken by 2nd to go 1,320 ft, OR\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200%2FS%5B1%5D+=+1320%2FS%5B2%5D ALIGN=MIDDLE  ALT=\"1200%2FS%5B1%5D+=+1320%2FS%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200S%5B2%5D+=+1320S%5B1%5D ALIGN=MIDDLE  ALT=\"1200S%5B2%5D+=+1320S%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- Cross-multiplying ---- eq (ii)\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1120S%5B2%5D+%2B+4S%5B1%5DS%5B2%5D+=+1200S%5B2%5D ALIGN=MIDDLE  ALT=\"1120S%5B2%5D+%2B+4S%5B1%5DS%5B2%5D+=+1200S%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- ----- Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200S%5B2%5D ALIGN=MIDDLE  ALT=\"1200S%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1320S%5B1%5D ALIGN=MIDDLE  ALT=\"1320S%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > in eq (i)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28280S%5B2%5D+%2B+S%5B1%5DS%5B2%5D%29+=+4%28300S%5B2%5D%29 ALIGN=MIDDLE  ALT=\"4%28280S%5B2%5D+%2B+S%5B1%5DS%5B2%5D%29+=+4%28300S%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- Factoring out GCF, 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=280S%5B2%5D+%2B+S%5B1%5DS%5B2%5D+=+300S%5B2%5D ALIGN=MIDDLE  ALT=\"280S%5B2%5D+%2B+S%5B1%5DS%5B2%5D+=+300S%5B2%5D\"   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=S%5B1%5DS%5B2%5D+=+300S%5B2%5D+-+280S%5B2%5D ALIGN=MIDDLE  ALT=\"S%5B1%5DS%5B2%5D+=+300S%5B2%5D+-+280S%5B2%5D\"   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=S%5B1%5DS%5B2%5D+=+20S%5B2%5D ALIGN=MIDDLE  ALT=\"S%5B1%5DS%5B2%5D+=+20S%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B2%5D%28S%5B1%5D%29+=+S%5B2%5D%2820%29 ALIGN=MIDDLE  ALT=\"S%5B2%5D%28S%5B1%5D%29+=+S%5B2%5D%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- Factoring out GCF, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B2%5D ALIGN=MIDDLE  ALT=\"S%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B1%5D++=+20 ALIGN=MIDDLE  ALT=\"S%5B1%5D++=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B1%5D ALIGN=MIDDLE  ALT=\"S%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or speed of 1st runner = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2820%29 ALIGN=MIDDLE  ALT=\"highlight_green%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft/s \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200S%5B2%5D+=+1320%2820%29 ALIGN=MIDDLE  ALT=\"1200S%5B2%5D+=+1320%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- Substituting 20 for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B1%5D ALIGN=MIDDLE  ALT=\"S%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > in eq (ii)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200S%5B2%5D+=+26400 ALIGN=MIDDLE  ALT=\"1200S%5B2%5D+=+26400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B2%5D ALIGN=MIDDLE  ALT=\"S%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or speed of 2nd runner = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26400%2F1200 ALIGN=MIDDLE  ALT=\"26400%2F1200\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2822%29 ALIGN=MIDDLE  ALT=\"highlight_green%2822%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft/s\r<BR>\n" );
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document.write( "You can do the check!!\r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at MathMadEzy@aol.com </SPAN>\n" );
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