document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258041>Question 258041</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person traveling 4hr 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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189888 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=189888\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is an RTD problem. Let RS = rate of ship, and Rp = rate of plane. Here is a table based on the given information:<BR>\n" );
document.write( "transport . . . . . . . .rate . . . . . . . .time . . . . . . .distance<BR>\n" );
document.write( "PLANE . . . . . . . . . .Rp . . . . . . . . .4 . . . . . . . . .4Rp<BR>\n" );
document.write( "SHIP . . . . . . . . . .Rs . . . . . . . . . .25 . . . . . . . . 25Rs<BR>\n" );
document.write( "TOTAL . . . . . . . . . . . . . . . . . . . .29 . . . . . . . . .1580<BR>\n" );
document.write( "So, we get from column 3,<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4Rp+%2B+25Rs+=+1580 ALIGN=MIDDLE  ALT=\"4Rp+%2B+25Rs+=+1580\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We are now given additional information and it looks like this:<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29Rp%2A4+%2B+%285%2F4%29Rs%2A25+=+1315 ALIGN=MIDDLE  ALT=\"%281%2F2%29Rp%2A4+%2B+%285%2F4%29Rs%2A25+=+1315\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply (ii) by 2 and we get<BR>\n" );
document.write( "(iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4Rp+%2B+62.5Rs+=+2630 ALIGN=MIDDLE  ALT=\"4Rp+%2B+62.5Rs+=+2630\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve (i) for 4Rp and we get<BR>\n" );
document.write( "(iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4Rp+=+1580+-+25Rs ALIGN=MIDDLE  ALT=\"4Rp+=+1580+-+25Rs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substituting (iv) into (iii), we get<BR>\n" );
document.write( "(v) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1580+-+25Rs+%2B+62.5Rs+=+2630 ALIGN=MIDDLE  ALT=\"1580+-+25Rs+%2B+62.5Rs+=+2630\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solving for Rs, we get<BR>\n" );
document.write( "(vi) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1580+%2B37.5Rs+=+2630 ALIGN=MIDDLE  ALT=\"1580+%2B37.5Rs+=+2630\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then<BR>\n" );
document.write( "(vii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37.5Rs+=+1050 ALIGN=MIDDLE  ALT=\"37.5Rs+=+1050\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, <BR>\n" );
document.write( "Rs = 28<BR>\n" );
document.write( "and <BR>\n" );
document.write( "Rp = 220.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );