document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120766>Question 120766</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person traveling 4 hours by plane and 25 hours by ship covers 1580 miles.  If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have traveled only 1315 miles in the same length of time.  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 #88573 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=88573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A person traveling 4 hours by plane and 25 hours by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have traveled only 1315 miles in the same length of time. Find the speeds of the plane and the ship.<BR>\n" );
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document.write( "Let x = original speed of the plane<BR>\n" );
document.write( "Let y = original speed of the ship<BR>\n" );
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document.write( "Then:<BR>\n" );
document.write( ".5x = the \"if\" speed of the plane<BR>\n" );
document.write( "1.25y = the \"if\" speed of the ship<BR>\n" );
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document.write( "An equation for the statement:<BR>\n" );
document.write( "\"A person traveling 4 hours by plane and 25 hours by ship covers 1580 miles.\" <BR>\n" );
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document.write( "4x + 25y = 1580; call it the original equation<BR>\n" );
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document.write( "An equation for the statement:<BR>\n" );
document.write( " \"If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have traveled only 1315 miles in the same length of time.\"\r<BR>\n" );
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document.write( "4(.5x) + 25(1.25y) = 1315<BR>\n" );
document.write( "2x + 31.25y = 1315; call it the \"If\" equation<BR>\n" );
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document.write( "Multiply the above equation by 2 and subtract the original equation<BR>\n" );
document.write( "4x + 62.5y = 2630<BR>\n" );
document.write( "4x +  25y = 1580<BR>\n" );
document.write( "-------------------subtracting eliminates x, find y:<BR>\n" );
document.write( "0x + 37.5y = 1050<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1050%2F37.5 ALIGN=MIDDLE  ALT=\"1050%2F37.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 28 mph is the original speed of the ship<BR>\n" );
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document.write( "Use the original equation to find the speed of the plane<BR>\n" );
document.write( "4x + 25(28) = 1580<BR>\n" );
document.write( "4x = 1580 - 700<BR>\n" );
document.write( "4x = 880<BR>\n" );
document.write( "x = 220 mph is the original speed of the plane<BR>\n" );
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document.write( "You can check the solution in the \"if\" equation<BR>\n" );
document.write( "2(220) + 31.25(28) =  </SPAN>\n" );
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