document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=509175>Question 509175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 26.Solve.<BR>\n" );
document.write( "15t^2 + 7t = 2\r<BR>\n" );
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document.write( "Solve:#14<BR>\n" );
document.write( "Rowing. Abby rows 10 km upstream and 10 km back in a total time of 3 hr. The speed of the river is 5 km/h. Find Abby’s speed in still water.\r<BR>\n" );
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document.write( "My math friends please help me with these I am on a deadline, thank you.I really am desperate here. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #341319 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=341319\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "26.  Add -2 to both sides.  Then factor.  3 times 5 is 15, 2 times -1 is -2, 3 times -1 plus 5 times 2 is -3 plus 10 equals 7.\r<BR>\n" );
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document.write( "14.  Use distance = rate times time which can also be expressed as time equals distance divided by rate.  If you let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> represent the speed in still water, then the upstream rate is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\ -\ 5\"> because the current works against you going upstream and the downstream rate is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\ +\ 5\">.  Then let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> represent the time it took to go upstream.  Since the total trip took 3 hours, the time to go downstream must be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3\ -\ t\">.\r<BR>\n" );
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document.write( "First describe the upstream trip using time equals distance divided by rate:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{10}{r\ -\ 5}\">\r<BR>\n" );
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document.write( "Then describe the downstream trip the same way:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3\ -\ t\ =\ \frac{10}{r\ +\ 5}\"> \r<BR>\n" );
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document.write( "A little Algebra music, Sammy (while we isolate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> in that second equation):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ 3\ -\ \frac{10}{r\ +\ 5}\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{3r\ +\ 15\ -\ 10}{r\ +\ 5}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{3r\ +\ 5}{r\ +\ 5}\"> \r<BR>\n" );
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document.write( "Now we have two expressions that equate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> to something, so set the two right-hand sides equal:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{10}{r\ -\ 5}\ =\ \frac{3r\ +\ 5}{r\ +\ 5}\">\r<BR>\n" );
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document.write( "A little more Algebra music while we cross-multiply the proportion and collect like terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10(r\ +\ 5)\ =\ (r\ -\ 5)(3r\ +\ 5)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10r\ +\ 50\ =\ 3r^2\ -\ 10r\ -\ 25\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3r^2\ -\ 20r\ -\ 75\ =\ 0\">\r<BR>\n" );
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document.write( "This ugly thing will defy all of your efforts to factor it, so it is time for the -- Look!  Up in the sky!  It's a bird!  It's a plane!  It's - it's SuperQuadratic Formula! -- the Quadratic Formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ r\ =\ \frac{-b\ \pm\ \sqrt{b^2\ -\ 4ac}}{2a}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ r\ =\ \frac{-(-20)\ \pm\ \sqrt{-20^2\ -\ 4(3)(-75)}}{2(3)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{20\ \pm\ \sqrt{400\ +\ 900}}{6}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{10\ \pm\ 5\sqrt{13}}{3}\">\r<BR>\n" );
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document.write( "A little calculator work will show you that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{10\ -\ 5\sqrt{13}}{3}\ < 0\">\r<BR>\n" );
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document.write( "and since it is unlikely that Abby got anywhere rowing backwards, we can safely discard this root leaving us with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{10\ +\ 5\sqrt{13}}{3}\">\r<BR>\n" );
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document.write( "As the exact answer.  Use your calculator to obtain a numerical approximation to the precision you require.<BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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