document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66725>Question 66725</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1- a six passanger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind  then what is the wind speed?\r<BR>\n" );
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document.write( "2- Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour than Smith's. How fast was each one traveling ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #47376 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=47376\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1- a six passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind. in the same amount of time as it flies 5 miles against the wind, then what is the wind speed?<BR>\n" );
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document.write( "Let x = wind speed:<BR>\n" );
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document.write( "Speed against the wind = (180-x)<BR>\n" );
document.write( "Speed with the wind = (180+x)<BR>\n" );
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document.write( "Write a time equation: time = dist/speed<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28%28180-x%29%29 ALIGN=MIDDLE  ALT=\"5%2F%28%28180-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%28%28180%2Bx%29%29 ALIGN=MIDDLE  ALT=\"7%2F%28%28180%2Bx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cross multiply and you have:<BR>\n" );
document.write( "5(180+x) = 7(180-x)<BR>\n" );
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document.write( "900 + 5x = 1260 - 7x<BR>\n" );
document.write( "5x + 7x = 1260 - 900<BR>\n" );
document.write( "12x = 360<BR>\n" );
document.write( "x = 360-12<BR>\n" );
document.write( "x = 30 mph speed of the wind:<BR>\n" );
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document.write( "Check: 5/150 = 7/210<BR>\n" );
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document.write( "2- Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour than Smith's. How fast was each one traveling ?<BR>\n" );
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document.write( "I understand this to mean: <BR>\n" );
document.write( "Jones' 70 mi trip took a half hr longer than Smith's 45 mi trip<BR>\n" );
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document.write( "Let Smith's speed = s<BR>\n" );
document.write( "Then Jones' speed = (s+5)<BR>\n" );
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document.write( "Write a time equation again:<BR>\n" );
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document.write( "Smith's time + .5 hr = Jones' time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2Fs+%2B+1%2F2 ALIGN=MIDDLE  ALT=\"45%2Fs+%2B+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( "Get rid of the denominators by multiplying equation by 2s(s+5), you then 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<BR>\n" );
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document.write( "This quadratic equation will factor to:<BR>\n" );
document.write( "(s-30)(s-15) = 0<BR>\n" );
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document.write( "s = 30 mph or s = 15 mph<BR>\n" );
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document.write( "Both solutions will work, however, practically the bike av speed would be:<BR>\n" );
document.write( "Smith: 15 mph and Jones: 20 mph, I would think<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "Jones time - Smiths time<BR>\n" );
document.write( "70/20 - 45/15 =<BR>\n" );
document.write( " 3.5 hr - 3 hr = 1/2 hr\r<BR>\n" );
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