document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145797>Question 145797</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person traveling 4 hr by plane and 25 hr 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 #106435 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=106435\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  person traveling 4 hr by plane and 25 hr 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 = speed of the plane<BR>\n" );
document.write( "and<BR>\n" );
document.write( "Let y = speed of the boat<BR>\n" );
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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.\"<BR>\n" );
document.write( "Then<BR>\n" );
document.write( ".5x = speed of the plane<BR>\n" );
document.write( "and<BR>\n" );
document.write( "1.25y = speed of the boat<BR>\n" );
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document.write( "When they say,\" the person would have traveled only 1315 miles in the same length of time.\" <BR>\n" );
document.write( "I assume they still mean 4 hrs in the plane and 25 hrs in the boat.<BR>\n" );
document.write( "If they mean only that the total time is 29 hrs it's a different problem.<BR>\n" );
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document.write( "Two equations:<BR>\n" );
document.write( "4x + 25y = 1580<BR>\n" );
document.write( "and<BR>\n" );
document.write( ".5(4x) + 1.25(25y) = 1315<BR>\n" );
document.write( "    2x + 31.25y = 1315<BR>\n" );
document.write( "Multiply this equation by 2 and subtract the 1st equation from it<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( "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 speed of the boat<BR>\n" );
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document.write( "Find the speed of the plane using the 1st equation:<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( "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 is the speed of the plane<BR>\n" );
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document.write( "Check using the \"if\" situation:<BR>\n" );
document.write( "4(110) + 25(35) = 1315<BR>\n" );
document.write( " </SPAN>\n" );
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