document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=89511>Question 89511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I just need help setting up the equation. It's from Algebra, Part 3 from Thomson Education Direct. It's a career oriented study unit. # of book is 2469C-1\r<BR>\n" );
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document.write( "A person travels 4 hrs by plane and 25 hrs by ship and covers a total distance of 1580 miles. If the plane's speed would have been 1/2 of the actual speed and the ship's speed 1/4 greater than the actual speed, a distance of 1315 miles would have been travelled. Find the speeds of the plane and the ship. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65065 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=65065\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A person travels 4 hrs by plane and 25 hrs by ship and covers a total distance of 1580 miles. If the plane's speed would have been 1/2 of the actual speed and the ship's speed 1/4 greater than the actual speed, a distance of 1315 miles would have been traveled. Find the speeds of the plane and the ship.<BR>\n" );
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document.write( "Let x = actual speed of the plane; and: y = actual speed of the ship<BR>\n" );
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document.write( "Write 2 distance equations; Dist = time * speed:<BR>\n" );
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document.write( "4x + 25y = 1580; actual speed equation<BR>\n" );
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document.write( "We also have:<BR>\n" );
document.write( "\"If the plane's speed would have been 1/2 of the actual speed and the ship's speed 1/4 greater than the actual speed, a distance of 1315 miles \"<BR>\n" );
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document.write( "Equation for this would be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%29 ALIGN=MIDDLE  ALT=\"1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*4x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4 ALIGN=MIDDLE  ALT=\"5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >*25y = 1315<BR>\n" );
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document.write( "Mult equation by 4 to get rid of these fractions and we have:<BR>\n" );
document.write( "2(4x) + 5(25y) = 5260<BR>\n" );
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document.write( "8x + 125y = 5260; the \"if...\" equation<BR>\n" );
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document.write( "Multiply the actual equation by 2 and subtract it from the above equation<BR>\n" );
document.write( "8x + 125y = 5260<BR>\n" );
document.write( "8x +  50y = 3160<BR>\n" );
document.write( "---------------- subtraction eliminates x<BR>\n" );
document.write( "0x + 75y = 2100<BR>\n" );
document.write( "y = 2100/75<BR>\n" );
document.write( "y = 28 mph is the ships speed<BR>\n" );
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document.write( "Use the actual speed equation to find x<BR>\n" );
document.write( "4x + 25(28) = 1580<BR>\n" );
document.write( "4x + 700 = 1580<BR>\n" );
document.write( "4x = 1580 - 700<BR>\n" );
document.write( "4x = 880<BR>\n" );
document.write( "x = 880/4<BR>\n" );
document.write( "x = 220 mph is the speed of the plane<BR>\n" );
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document.write( "Check solutions in the \"if..\" equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%29 ALIGN=MIDDLE  ALT=\"1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*4(220) + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4 ALIGN=MIDDLE  ALT=\"5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >*25(28) = 1315<BR>\n" );
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document.write( "440 + 875 = 1315<BR>\n" );
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document.write( " </SPAN>\n" );
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