document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161535>Question 161535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> togo flew his ultralight plane to a landing field 30 mi away. With the wind, the flight took 3/5h. Returning against the wind, the flight took 5/6h. Find the rate of the plane in still air and the rate of the wind. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119007 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=119007\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> togo flies 30 miles in 3/5 of an hour with the wind.<BR>\n" );
document.write( "togo flies 30 miles in 5/6 of an hour against the wind.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "his rate of speed with the wind was 30 / (3/5) = 30*5/3 = 150/3 = 50 mph.<BR>\n" );
document.write( "his rate of speed against the wind was 30 / (5/6) = 30*6/5 = 6*6 = 36 mph.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "3/5 of an hour times 50 mph = 30 miles.<BR>\n" );
document.write( "5/6 of an hour times 36 mph = 30 miles.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "mph looks good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "going he was with the wind.<BR>\n" );
document.write( "his rate of speed then was the airplane speed plus the wind speed.<BR>\n" );
document.write( "coming back he was against the wind.<BR>\n" );
document.write( "his rate of speed then was the airplane speed minus the wind speed.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "50 mph = A + W<BR>\n" );
document.write( "36 mph = A - W<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "looks like A + W - (A - W) should equal 50 - 36.<BR>\n" );
document.write( "removing parentheses, equation becomes<BR>\n" );
document.write( "A + W - A + W = 14.<BR>\n" );
document.write( "combining like terms, the equation becomes<BR>\n" );
document.write( "2*W = 14.<BR>\n" );
document.write( "dividing both sides by 2, equation becomes<BR>\n" );
document.write( "W = 7.<BR>\n" );
document.write( "if W = 7, then A can be found as follows:<BR>\n" );
document.write( "50 = A + 7<BR>\n" );
document.write( "A = 43.<BR>\n" );
document.write( "likewise,<BR>\n" );
document.write( "36 = A - 7<BR>\n" );
document.write( "A = 43.<BR>\n" );
document.write( "since the airplane speed is the same, it looks like the answer is good.<BR>\n" );
document.write( "solving in the original equations, we get<BR>\n" );
document.write( "3/5 * (43 + 7) = 30<BR>\n" );
document.write( "3/5 * 50- = 30<BR>\n" );
document.write( "30 = 30<BR>\n" );
document.write( "good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "5/6 * (43 - 7) = 30<BR>\n" );
document.write( "5/6 * 36 = 30<BR>\n" );
document.write( "30 = 30<BR>\n" );
document.write( "good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer is W = 7 and A = 43. </SPAN>\n" );
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