document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126254>Question 126254</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person traveling 4 hour by plane and 25 hour by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and 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 #92619 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=92619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A person traveling 4 hour by plane and 25 hour by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and 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( "Originally<BR>\n" );
document.write( "Let x = speed of the plane (mph)<BR>\n" );
document.write( "Let y = speed of the ship<BR>\n" );
document.write( "If:<BR>\n" );
document.write( ".5x = speed of the plane<BR>\n" );
document.write( "1.25y = speed of the ship<BR>\n" );
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document.write( "Write two distance equations: Distance = time * speed<BR>\n" );
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document.write( "Actual event equation:<BR>\n" );
document.write( "4x + 25y = 1580<BR>\n" );
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document.write( "If event equation:<BR>\n" );
document.write( "4(.5x) + 25(1.25y)<BR>\n" );
document.write( "2x + 31.25y = 1315 <BR>\n" );
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document.write( "Use elimination here. Multiple above equation by 2, subtract \"Actual\" equation:<BR>\n" );
document.write( "4x + 62.5y = 2630<BR>\n" );
document.write( "4x + 25y = 1580<BR>\n" );
document.write( "-------------------Subtracting eliminates x<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 ships original speed<BR>\n" );
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document.write( "Use equation; 4x + 25y = 1580; substitute 28 for y:<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 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=880%2F4 ALIGN=MIDDLE  ALT=\"880%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 220 mph plane's original speed<BR>\n" );
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document.write( "Check our solutions in the \"If event\" equation<BR>\n" );
document.write( "4(.5(220)) + 25(1.25(28)) = <BR>\n" );
document.write( "440 + 875 = 1315 </SPAN>\n" );
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