document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88386>Question 88386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to solve the following equations: \r<BR>\n" );
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document.write( "Solve each formula for the indicated variable:\r<BR>\n" );
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document.write( "18)  I= E/R+r for R\r<BR>\n" );
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document.write( "Please find the value of the indicated variable:\r<BR>\n" );
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document.write( "Please show a complete solution to each problem. \r<BR>\n" );
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document.write( "36)  Ride the peaks.  Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles.  Jones averaged 5 miles per hour than smith, and his trip took one-half hour longer that Smith's.  How fast was each one traveling?\r<BR>\n" );
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document.write( "Thank you so much for your assistance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64193 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=64193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve each formula for the indicated variable:<BR>\n" );
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document.write( "Assume you mean:<BR>\n" );
document.write( "I = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%2F%28%28R%2Br%29%29 ALIGN=MIDDLE  ALT=\"E%2F%28%28R%2Br%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for R<BR>\n" );
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document.write( "Multiply both sides by (R+r) and you have:<BR>\n" );
document.write( "I(R+r) = E<BR>\n" );
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document.write( "Divide both sides by I and you have:<BR>\n" );
document.write( "R + r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%2FI ALIGN=MIDDLE  ALT=\"E%2FI\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract r from both sides:<BR>\n" );
document.write( "R = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28E%2FI%29 ALIGN=MIDDLE  ALT=\"%28E%2FI%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - r<BR>\n" );
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document.write( "36) Ride the peaks. Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour than smith, and his trip took one-half hour longer that Smith's. How fast was each one traveling? <BR>\n" );
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document.write( "Kind of a poorly worded problem, I interpret it to mean:<BR>\n" );
document.write( "It took Jones a half hour longer to travel 70 mi than Smith to travel 45 mi<BR>\n" );
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document.write( "Let s = smith's speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+5) = Jone's speed<BR>\n" );
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document.write( "Write a time equation;Time = Dist/time<BR>\n" );
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document.write( "Smith's 45 mi time + half hr = Jone's 70 mi time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2Fs ALIGN=MIDDLE  ALT=\"45%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F%28%28s%2B5%29%29 ALIGN=MIDDLE  ALT=\"70%2F%28%28s%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply equation by 2s(s+5) to get rid of the denominators, we have:<BR>\n" );
document.write( "45*2(s+5) + s(s+5) = 70*2s<BR>\n" );
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document.write( "90s + 450 + s^2 + 5s = 140s<BR>\n" );
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document.write( "s^2 + 90s + 5s - 140s + 450 = 0<BR>\n" );
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document.write( "s^2 - 45s + 450 = 0; a quadratic equation<BR>\n" );
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document.write( "Factors to:<BR>\n" );
document.write( "(s - 15)(s - 30) = 0<BR>\n" );
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document.write( "s = 15<BR>\n" );
document.write( "and <BR>\n" );
document.write( "s = 30<BR>\n" );
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document.write( "Check both solutions<BR>\n" );
document.write( "s = 15, then j = 20<BR>\n" );
document.write( "45/15 = 3 hr<BR>\n" );
document.write( "70/20 = 3.5 hr<BR>\n" );
document.write( "and<BR>\n" );
document.write( "s = 30, j = 35<BR>\n" );
document.write( "45/30 = 1.5 hrs<BR>\n" );
document.write( "70/35 = 2.0 hr<BR>\n" );
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document.write( "Interesting that both solution work, isn't it?\r<BR>\n" );
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document.write( " </SPAN>\n" );
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