document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161627>Question 161627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi to all of you who help. can you please help me?  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 ship.thanks for the help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119120 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=119120\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = rate of the plane.<BR>\n" );
document.write( "let y = rate of the ship.<BR>\n" );
document.write( "first equation is:<BR>\n" );
document.write( "4*x + 25*y = 1580.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the plane traveled 4 hours at half rate of speed, and the ship traveled 25 hours at 1.25 rate of speed, the second equation becomes<BR>\n" );
document.write( "2*x + 31.25*y = 1315.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this is because 4 * x/2 = 2*x, and 25 * (5/4*y) = 125/4 * y = 31.25 * y.<BR>\n" );
document.write( "the distance traveled under these new rates of speed is 1315.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we have 2 equations with 2 unknowns.<BR>\n" );
document.write( "4*x + 25*y = 1580<BR>\n" );
document.write( "2*x + 31.25*y = 1315.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiply the bottom equation by 2 so we can eliminate the x.<BR>\n" );
document.write( "equations become<BR>\n" );
document.write( "4*x + 25*y = 1580<BR>\n" );
document.write( "4*x + 62.5*y = 2630<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "subtract top equation from bottom equation to get<BR>\n" );
document.write( "37.5*y = 1050<BR>\n" );
document.write( "y = 28<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if y = 28, we can solve for x in either equation.<BR>\n" );
document.write( "use 4*x + 25*y = 1580<BR>\n" );
document.write( "this becomes<BR>\n" );
document.write( "4*x + 700 = 1580<BR>\n" );
document.write( "4*x = 880<BR>\n" );
document.write( "x = 220<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x = 220 = rate of plane<BR>\n" );
document.write( "y = 28 = rate of ship<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove, take 1/2 the rate of the plane and 1.25 times the rate of the ship to solve the second equation.<BR>\n" );
document.write( "1/2 * 220 = 110.<BR>\n" );
document.write( "5/4 * 28 = 35<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "4*110 + 25*35 = 1315 which proves the values of x and y are good in both equations.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "plane travels at 220 miles per hour for 4 hours.<BR>\n" );
document.write( "ship travels at 28 miles per hour for 25 hours.<BR>\n" );
document.write( "total distance traveled is 1580 miles.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "plane travels at 110 miles per hour for 4 hours.<BR>\n" );
document.write( "ship travels at 35 miles per hour for 25 hours.<BR>\n" );
document.write( "total distance traveled is 1315 miles.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "110 is half of 220.<BR>\n" );
document.write( "35 is 5/4 * 28.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x = 220<BR>\n" );
document.write( "y = 28\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );