document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107934>Question 107934</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 #78733 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=78733\">put this solution on YOUR website!</A><BR><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.<BR>\n" );
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document.write( "Let x = speed of the plane<BR>\n" );
document.write( "Let y = 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\" equation:<BR>\n" );
document.write( "4x + 25y = 1580<BR>\n" );
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document.write( "The \"If\" equation:<BR>\n" );
document.write( ".5(4x) + 1.25(25y) = 1315<BR>\n" );
document.write( "or<BR>\n" );
document.write( "2x + 31.25y = 1315<BR>\n" );
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document.write( "Multiply the above equation by 2, subtract the \"actual\" equation<BR>\n" );
document.write( "4x + 62.5y = 2630<BR>\n" );
document.write( "4x + 25.0y = 1580<BR>\n" );
document.write( "------------------- subtracting eliminates x<BR>\n" );
document.write( "0x + 37.5y = 1050<BR>\n" );
document.write( "y = 1050/37.5<BR>\n" );
document.write( "y = 28 mph is the actual speed of the ship<BR>\n" );
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document.write( "Find x using the \"actual\" 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 = 880/4<BR>\n" );
document.write( "x = 220 mph is the actual speed of the plane\r<BR>\n" );
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document.write( "Check solution using the \"IF\" equation<BR>\n" );
document.write( ".5(4*220) + 1.25(25*28) =<BR>\n" );
document.write( "440  + 875 = 1315 </SPAN>\n" );
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