document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=426858>Question 426858</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 0ne-fourth greater, the person would have traveled only 1315 miles in the same length of time. What is the speed 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 #296884 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=296884\">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<BR>\n" );
document.write( " speed of the plane had been one-half of the actual speed and the speed of the<BR>\n" );
document.write( " ship had  been one-forth greater, the person would have traveled only 1315<BR>\n" );
document.write( " miles in the same length of time. Find the speeds of the plane and the ship.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = speed of plane<BR>\n" );
document.write( "and<BR>\n" );
document.write( "Let y = speed of ship<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Two distance equations; dist = time * speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "4x + 25y = 1580<BR>\n" );
document.write( "and<BR>\n" );
document.write( "4(.5x) + 25(1.25y) = 1315, (plane half speed, boat 1.25 original speed)<BR>\n" );
document.write( "2x + 31.25y = 1315<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply above equation by 2. Subtract the first equation<BR>\n" );
document.write( "4x + 62.5y = 2630<BR>\n" );
document.write( "4x +  25y =  1580<BR>\n" );
document.write( "---------------------subtraction eliminates x, find y:<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 speed of the ship <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find x 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( "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 speed of the plane<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution in 2nd equation, plane half speed, boat 1.25 original speed:<BR>\n" );
document.write( "4(110) + 25(35) = <BR>\n" );
document.write( "440 + 875 = 1315 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );