document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205963>Question 205963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Ramesh walks at 5/6th of his usual speed and reaches school 4 minutes late. Find the usual time taken by him to reach school.<BR>\n" );
document.write( "2. Rakesh runs at 5/4 of his usual speed and reaches the playground 5 minutes earlier. What is his usual time/<BR>\n" );
document.write( "3.Two trains 110m and 100m long are running on parallel tracks, in the same direction with a speed of 46 km/hr and 39 km/hr respectively. How long will it take them to be clear of each other?<BR>\n" );
document.write( "4. A cyclist A started his journey on cycle at 7.30 a.m. at speed 8km/hr. B another cyclist started from the same point half an hour later but with speed 10 km/hr. At what time did B overtake A? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155580 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=155580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Ramesh walks at 5/6th of his usual speed and reaches school 4 minutes late.<BR>\n" );
document.write( " Find the usual time taken by him to reach school.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = usual walking speed <BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >s = slower speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let t = usual time to walk to school<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t+4) = time required when walking slower<BR>\n" );
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document.write( "write a distance equation<BR>\n" );
document.write( "ts = (t+4)(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >s)<BR>\n" );
document.write( ";<BR>\n" );
document.write( "multiply both sides by 6<BR>\n" );
document.write( "6ts = 5s(t+4)<BR>\n" );
document.write( "6ts = 5ts + 20s<BR>\n" );
document.write( "6ts - 5ts = 20s<BR>\n" );
document.write( "ts = 20s<BR>\n" );
document.write( "Divide for sides by s, results<BR>\n" );
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document.write( "t = 20 min; normal time to walk to school<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2. Rakesh runs at 5/4 of his usual speed and reaches the playground 5 minutes earlier. <BR>\n" );
document.write( "What is his usual time/<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = usual running speed <BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4 ALIGN=MIDDLE  ALT=\"5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >s = faster running speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let t = usual time to run to school<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t-5) = time required when running faster<BR>\n" );
document.write( ":<BR>\n" );
document.write( "write a distance equation<BR>\n" );
document.write( "ts = (t-5)(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4 ALIGN=MIDDLE  ALT=\"5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >s)<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Multiply both side by 4<BR>\n" );
document.write( "4ts = 5s(t-5)<BR>\n" );
document.write( "4ts = 5ts - 25s<BR>\n" );
document.write( "4ts - 5ts = -25s<BR>\n" );
document.write( "-ts = -25s<BR>\n" );
document.write( "Divide for sides by -s, results<BR>\n" );
document.write( ":<BR>\n" );
document.write( "t = 25 min; normal time running to school<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "3.Two trains 110m and 100m long are running on parallel tracks, in the same<BR>\n" );
document.write( " direction with a speed of 46 km/hr and 39 km/hr respectively.<BR>\n" );
document.write( " How long will it take them to be clear of each other?<BR>\n" );
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document.write( "The relative speed between the two trains: 46 - 39 = 7 km/hr<BR>\n" );
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document.write( "How long to travel 110+100 = 210m at 7 km/hr?<BR>\n" );
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document.write( "210 m = .21 km: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.21%2F7 ALIGN=MIDDLE  ALT=\".21%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > * 60 ~ 1.8 minutes<BR>\n" );
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document.write( ":<BR>\n" );
document.write( "4. A cyclist A started his journey on cycle at 7.30 a.m. at speed 8km/hr.<BR>\n" );
document.write( " B another cyclist started from the same point half an hour later but with<BR>\n" );
document.write( " speed 10 km/hr.<BR>\n" );
document.write( " At what time did B overtake A?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let t = B's travel time<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t+.5) = A's travel time<BR>\n" );
document.write( ":<BR>\n" );
document.write( "When B overtakes A, they will have traveled the same distance<BR>\n" );
document.write( "Write a distance equation<BR>\n" );
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document.write( "10t = 8(t+.5)<BR>\n" );
document.write( "10t = 8t + 4<BR>\n" );
document.write( "10t - 8t = 4<BR>\n" );
document.write( "2t = 4<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F2 ALIGN=MIDDLE  ALT=\"4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 2 hrs is B's travel time<BR>\n" );
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document.write( "He left at 8:00, therefore he overtakes A at 10:00<BR>\n" );
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document.write( "Check solution by ensuring their distances are equal<BR>\n" );
document.write( "2*10 = 20 km<BR>\n" );
document.write( "2.5* 8 = 20 km </SPAN>\n" );
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