document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=507878>Question 507878</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sam rode his bike for 1 mile to a friend's house.  Then his friend's mom drove him 12 miles at a rate that was 25 miles per hour faster than he was able to ride his bike.  If the entire trip took 3/5 of an hour, what was Sam's rate of speed on the bike? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #340880 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=340880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sam rode his bike for 1 mile to a friend's house.<BR>\n" );
document.write( " Then his friend's mom drove him 12 miles at a rate that was 25 miles per hour faster than he was able to ride his bike.<BR>\n" );
document.write( " If the entire trip took 3/5 of an hour, what was Sam's rate of speed on the bike?<BR>\n" );
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document.write( "Let b = bike speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(b+25) = car speed<BR>\n" );
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document.write( "Write a time equation, time = dist/speed<BR>\n" );
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document.write( "Bike time + car time = 3/5 hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fb ALIGN=MIDDLE  ALT=\"1%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28b%2B25%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28b%2B25%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply by 5b(b+25)<BR>\n" );
document.write( "5b(b+25)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fb ALIGN=MIDDLE  ALT=\"1%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 5b(b+25)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28b%2B25%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28b%2B25%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5b(b+25)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cancel out the denominators, resulting in<BR>\n" );
document.write( "5(b+25) + 5b(12) = 3b(b+25)<BR>\n" );
document.write( "5b + 125 + 60b = 3b^2 + 75b<BR>\n" );
document.write( "65b + 125 = 3b^2 + 75b<BR>\n" );
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document.write( "Arrange as a quadratic equation on the right<BR>\n" );
document.write( "0 = 3b^2 + 75b - 65b - 125<BR>\n" );
document.write( "3b^2 + 10b - 125 = 0<BR>\n" );
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document.write( "you can use the quadratic formula to find b, but this will factor;<BR>\n" );
document.write( "(3b+25)(b-5) = 0<BR>\n" );
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document.write( "the positive solution<BR>\n" );
document.write( "b = 5 mph is the bike speed<BR>\n" );
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document.write( ":<BR>\n" );
document.write( "Check this by finding that actual time of each<BR>\n" );
document.write( "5 + 25 = 30 mph is the cars speed<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F30 ALIGN=MIDDLE  ALT=\"12%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "Reduce fraction <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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