document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=684391>Question 684391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) Two trains X and Y enter at the same time a tunnel 1 Km. long at the opposite ends. They meet in 45 seconds, after X has travelled 200 meters more than Y. They cross each other in 4.5 seconds and 30 seconds later X is completely out of the tunnel. find the length and speed of each of the trains.\r<BR>\n" );
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document.write( "2) A train after travelling 50 Km. Meets with an accident and then proceeds at ¾ th of its former speed and arrives at its destination 35 minutes late. Had the accident happened 24 Km. Further on, it would have reached the destination only 23 minutes late. Find the speed of the train and the distance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #424105 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=424105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  1) Two trains X and Y enter at the same time a tunnel 1 Km long at the opposite ends.<BR>\n" );
document.write( " They meet in 45 seconds, after X has traveled 200 meters more than Y.<BR>\n" );
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document.write( "Find the distance each train has traveled when they meet<BR>\n" );
document.write( "let a = distance traveled by x when they meet<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(a-200) = distance traveled by y when they meet<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "a + (a-200) = 1000 meters<BR>\n" );
document.write( "2a = 1000 + 200<BR>\n" );
document.write( "2a = 1200<BR>\n" );
document.write( "a = 600 meters traveled by x, and 400 meters traveled by y<BR>\n" );
document.write( "then<BR>\n" );
document.write( "600/45 = 13.33 m/sec is the speed of x<BR>\n" );
document.write( "and<BR>\n" );
document.write( "400/45 = 8.89 m/sec is the speed of y<BR>\n" );
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document.write( "They cross each other in 4.5 seconds<BR>\n" );
document.write( "Find the total Length of the two trains<BR>\n" );
document.write( "L = 4.5(13.33+8.89)<BR>\n" );
document.write( "L = 100 meters<BR>\n" );
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document.write( " and 30 seconds later X is completely out of the tunnel.<BR>\n" );
document.write( "total time for x to enter and clear the tunnel<BR>\n" );
document.write( "45 + 4.5 + 30 = 79.5 seconds<BR>\n" );
document.write( "Find how far the train X travels in 79.5 sec at 13.33 m/sec<BR>\n" );
document.write( "79.5*13.333 = 1060 meters<BR>\n" );
document.write( "the tunnel is 1000 meters, therefore the train is 60 meters long<BR>\n" );
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document.write( "Find the length of y<BR>\n" );
document.write( "100 - 60 = 40 meters is the length of train y<BR>\n" );
document.write( ":<BR>\n" );
document.write( "find the length and speed of each of the trains.<BR>\n" );
document.write( "X is 60 meters long<BR>\n" );
document.write( "Y = 40 meters long<BR>\n" );
document.write( "and<BR>\n" );
document.write( "X = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813.333%2A3600%29%2F1000 ALIGN=MIDDLE  ALT=\"%2813.333%2A3600%29%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 48 km/hr<BR>\n" );
document.write( "Y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288.889%2A3600%29%2F1000 ALIGN=MIDDLE  ALT=\"%288.889%2A3600%29%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 32 km/hr<BR>\n" );
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document.write( "2) A train after traveling 50 Km. Meets with an accident and then proceeds at ¾ th of its former speed and arrives at its destination 35 minutes late.<BR>\n" );
document.write( "let s = train's normal speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( ".75s = train's speed after the the accident<BR>\n" );
document.write( "Let d = distance of the whole trip<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(d-50) = distance at a speed of .75s<BR>\n" );
document.write( "Write a time equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-50%29%2F%28.75s%29 ALIGN=MIDDLE  ALT=\"%28d-50%29%2F%28.75s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-50%29%2Fs ALIGN=MIDDLE  ALT=\"%28d-50%29%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2F60 ALIGN=MIDDLE  ALT=\"35%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply by 60s so get rid of the denominators, resulting in:<BR>\n" );
document.write( "80(d-50) - 60(d-50) = 35s<BR>\n" );
document.write( "80d - 4000 - 60d + 3000 = 35s<BR>\n" );
document.write( "20d - 35s - 1000 = 0<BR>\n" );
document.write( "20d - 35s = 1000<BR>\n" );
document.write( "then we are dealing with a distance of (d-74) <BR>\n" );
document.write( " Had the accident happened 24 Km. Further on, it would have reached the destination only 23 minutes late.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-74%29%2F%28.75s%29 ALIGN=MIDDLE  ALT=\"%28d-74%29%2F%28.75s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-74%29%2Fs ALIGN=MIDDLE  ALT=\"%28d-74%29%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23%2F60 ALIGN=MIDDLE  ALT=\"23%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply by 60s so get rid of the denominators, resulting in:<BR>\n" );
document.write( "80(d-74) - 60(d-74) = 23s<BR>\n" );
document.write( "80d - 5920 - 60d + 4440 = 23s<BR>\n" );
document.write( "20d - 23s - 1480 = 0<BR>\n" );
document.write( "20d - 23s = 1480<BR>\n" );
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document.write( "Use elimination here<BR>\n" );
document.write( "20d - 23s = 1480<BR>\n" );
document.write( "20d - 35s = 1000<BR>\n" );
document.write( "------------------subtraction eliminates d, find s<BR>\n" );
document.write( "12s = 480<BR>\n" );
document.write( "s = 480/12<BR>\n" );
document.write( "s = 40 km/hr is the normal speed (30 km/hr is the slower speed)<BR>\n" );
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document.write( "Find the speed of the train and the distance.<BR>\n" );
document.write( "20d - 23(40) = 1480<BR>\n" );
document.write( "20d - 920 = 1480<BR>\n" );
document.write( "20d = 1480 + 920<BR>\n" );
document.write( "20d = 2400<BR>\n" );
document.write( "d = 2400/20<BR>\n" );
document.write( "d = 120 km<BR>\n" );
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document.write( "Check that in the other equation<BR>\n" );
document.write( "20(120) - 35(40) = <BR>\n" );
document.write( "2400 - 1400 = 1000; confirms our solution of: <BR>\n" );
document.write( "speed: 40 km/hr, normal speed<BR>\n" );
document.write( "dist: 120 km  </SPAN>\n" );
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