document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122620>Question 122620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1)A jogger starts a course at a steady rate of 8 kph.Five minutes later,a second jogger starts the same course at 10 kph.How long will it take the second jogger to catch the first?\r<BR>\n" );
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document.write( "2)A man rows downstream at the rate of 5 mph and upstream at the rate of 2 mph.How far downstream should he go if he is to return in 7/4 hourse after leaving?\r<BR>\n" );
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document.write( "3)Two planes leave Manila for a southern city,a distance of 900 km.Plane A travels at a ground speed of 90 kph faster than the plane B.Plane A arrives in their destination 2 hours and 15 minutes ahead of Plane B.What is the ground speed of Plane A? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90073 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=90073\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)A jogger starts a course at a steady rate of 8 kph.Five minutes later,a second jogger starts the same course at 10 kph.How long will it take the second jogger to catch the first?<BR>\n" );
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document.write( "We are working in km/hr; change 5 min to hrs: 5/60 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > hr<BR>\n" );
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document.write( "Let t = time required by the 2nd jogger to catch up with the 1st<BR>\n" );
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document.write( "(t+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = travel time of the 1st jogger<BR>\n" );
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document.write( "When the 2nd jogger catches up with 1st, they will have traveled the same distance.<BR>\n" );
document.write( "Write a distance equation: Dist = speed * time<BR>\n" );
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document.write( "10t = 8(t+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "10t = 8t + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F12 ALIGN=MIDDLE  ALT=\"8%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "10t - 8t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hr which is 20 min<BR>\n" );
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document.write( "2)A man rows downstream at the rate of 5 mph and upstream at the rate of 2 mph. How far downstream should he go if he is to return in 7/4 hours after leaving?<BR>\n" );
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document.write( "Let d = distance one-way to return in 7/4 hrs<BR>\n" );
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document.write( "Write a time equation: time = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Distance%2Fspeed ALIGN=MIDDLE  ALT=\"Distance%2Fspeed\"   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=d%2F5 ALIGN=MIDDLE  ALT=\"d%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F2 ALIGN=MIDDLE  ALT=\"d%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F4 ALIGN=MIDDLE  ALT=\"7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the denominators, multiply equation by 20:<BR>\n" );
document.write( "20*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F5 ALIGN=MIDDLE  ALT=\"d%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 20*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F2 ALIGN=MIDDLE  ALT=\"d%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F4 ALIGN=MIDDLE  ALT=\"7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel out the denominators and you have:<BR>\n" );
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document.write( "4d + 10d = 5(7)<BR>\n" );
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document.write( "14d = 35<BR>\n" );
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document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2F14 ALIGN=MIDDLE  ALT=\"35%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = 2.5 mi he needs to row down stream to return in 7/4 hrs<BR>\n" );
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document.write( " 3)Two planes leave Manila for a southern city,a distance of 900 km. Plane A travels at a ground speed of 90 kph faster than the plane B. Plane A arrives in their destination 2 hours and 15 minutes ahead of Plane B. What is the ground speed of Plane A?<BR>\n" );
document.write( "Change 2 hr 15 min to hrs: 2.25 hrs<BR>\n" );
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document.write( "Let s = speed of plane A<BR>\n" );
document.write( "Then<BR>\n" );
document.write( "(s-90) = speed of plane B<BR>\n" );
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document.write( "Write a time equation: Time = distance/speed\r<BR>\n" );
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document.write( "Plane B's time - Plane A's = 2.25 hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900%2F%28%28s-90%29%29 ALIGN=MIDDLE  ALT=\"900%2F%28%28s-90%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900%2Fs ALIGN=MIDDLE  ALT=\"900%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" >} = 2.25<BR>\n" );
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document.write( "Get rid of the denominators, multiply equation by s(s-90)<BR>\n" );
document.write( "s(s-90)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900%2F%28%28s-90%29%29 ALIGN=MIDDLE  ALT=\"900%2F%28%28s-90%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - s(s-90)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900%2Fs ALIGN=MIDDLE  ALT=\"900%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = s(s-90)*2.25<BR>\n" );
document.write( "cancel out the denominator and you have:<BR>\n" );
document.write( "900s - 900(s-90) = 2.25(s^2 - 90s<BR>\n" );
document.write( "900s - 900s + 81000 = 2.25s^2 - 202.5s<BR>\n" );
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document.write( "Arrange as a quadratic equation:<BR>\n" );
document.write( "2.25s^2 - 202.5s - 81000<BR>\n" );
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document.write( "Simplify, divide equation by 2.25<BR>\n" );
document.write( "s^2 - 90s - 36000<BR>\n" );
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document.write( "This factors to:<BR>\n" );
document.write( "(s-240)(s+150) = 0<BR>\n" );
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document.write( "s = -150<BR>\n" );
document.write( "and<BR>\n" );
document.write( "s = +240 km/hr is our solution<BR>\n" );
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document.write( "I checked all three of these solutions on my calc. The reason I did not include<BR>\n" );
document.write( "the calculations here, is because of inexcusable laziness.  A </SPAN>\n" );
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