document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=493396>Question 493396</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a boy on his bicycle intends to arrive at a certain time to a town that is 30 km away from his home . after riding 10 km, he rested for half an hour and as a result he was obliged to ride the rest of the trip 2km/hr faster . what was his original speed ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #335383 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=335383\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a boy on his bicycle intends to arrive at a certain time to a town that is 30 km away from his home .<BR>\n" );
document.write( "after riding 10 km, he rested for half an hour and as a result he was obliged to ride the rest of the trip 2km/hr faster .<BR>\n" );
document.write( "what was his original speed?<BR>\n" );
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document.write( "Let s = his original speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+2) = his faster speed<BR>\n" );
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document.write( "Write a time equation; Time = dist/speed<BR>\n" );
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document.write( "Required time = faster time + half an hr <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2Fs ALIGN=MIDDLE  ALT=\"30%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F%28%28s%2B2%29%29 ALIGN=MIDDLE  ALT=\"30%2F%28%28s%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5<BR>\n" );
document.write( "multiply by s(s+2)<BR>\n" );
document.write( "s(s+2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2Fs ALIGN=MIDDLE  ALT=\"30%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = s(s+2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F%28%28s%2B2%29%29 ALIGN=MIDDLE  ALT=\"30%2F%28%28s%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5s(s+2)<BR>\n" );
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document.write( "Cancel the denominators<BR>\n" );
document.write( "30(s+2) = 30s + .5s^2 + 1s<BR>\n" );
document.write( "30s + 60 = 30s + .5s^2 + s<BR>\n" );
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document.write( "Arrange as quadratic equation on the right<BR>\n" );
document.write( "0 =.5s^2 + 30s - 30s + s - 60 <BR>\n" );
document.write( ".5s^2 + s - 60 = 0<BR>\n" );
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document.write( "multiply by 2 (make the coefficient of s^2 = 1, easier to factor)<BR>\n" );
document.write( "s^2 + 2s - 120 = 0<BR>\n" );
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document.write( "Factors to<BR>\n" );
document.write( "(s+12)(s-10) = 0<BR>\n" );
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document.write( "the positive solution<BR>\n" );
document.write( "s = 10 km/hr is his original speed<BR>\n" );
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document.write( "Check this by finding the actual time for each scenario<BR>\n" );
document.write( "30/10 = 3hrs<BR>\n" );
document.write( "30/12 = 2.5 hrs + half hr rest = 3hrs </SPAN>\n" );
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