document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204831>Question 1204831</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane made a two-way flight from Miami to Dublin.  The trip from Miami to Dublin took four more hours than the return trip from Dublin to Miami.  The cause for the difference in flight times were winds over the ocean, which averaged 50 km/hr on the return trip.  Assume there was no wind on the trip to Dublin.  The total distance travelled both ways was 9900 km. Let x represent the average speed of the plane in still air (no wind).<BR>\n" );
document.write( "a) Represent time going from Dublin to Miami as a rational expression.<BR>\n" );
document.write( "b) Represent the time going from Miami to Dublin as a rational expression.<BR>\n" );
document.write( "c) Write an equation representing the relationships between the times.<BR>\n" );
document.write( "d) What was the average rate of the plane in still air.<BR>\n" );
document.write( "e) How long did the round trip take? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841342 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841342\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "a) time = distance/speed: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4950%2Fx ALIGN=MIDDLE  ALT=\"4950%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "b) time = distance/speed: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4950%2F%28x-50%29 ALIGN=MIDDLE  ALT=\"4950%2F%28x-50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "c) time return trip at lower speed was 4 hours longer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4950%2F%28x-50%29=4950%2Fx%2B4 ALIGN=MIDDLE  ALT=\"4950%2F%28x-50%29=4950%2Fx%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "d) Solve the equation....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4950%2F%28x-50%29=4950%2Fx%2B4 ALIGN=MIDDLE  ALT=\"4950%2F%28x-50%29=4950%2Fx%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Clear fractions by multiplying by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%28x-50%29 ALIGN=MIDDLE  ALT=\"%28x%29%28x-50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4950x=4950%28x-50%29%2B4%28x%5E2-50x%29 ALIGN=MIDDLE  ALT=\"4950x=4950%28x-50%29%2B4%28x%5E2-50x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-200x-247500=0 ALIGN=MIDDLE  ALT=\"4x%5E2-200x-247500=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-50x-61875=0 ALIGN=MIDDLE  ALT=\"x%5E2-50x-61875=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Trying to solve that equation by factoring will take a long time; possibly the best way to finish the problem is to use a graphing calculator or some other tool.<br><BR>\n" );
document.write( "Or here is an algebraic technique that you can use to work this kind of problem.<br><BR>\n" );
document.write( "We are looking for two numbers whose difference is 50 and whose product is 61875.<br><BR>\n" );
document.write( "Let the two numbers that differ by 50 be y+25 and y-25.  Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B25%29%28y-25%29=61875 ALIGN=MIDDLE  ALT=\"%28y%2B25%29%28y-25%29=61875\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-625=61875 ALIGN=MIDDLE  ALT=\"y%5E2-625=61875\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=62500 ALIGN=MIDDLE  ALT=\"y%5E2=62500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=250 ALIGN=MIDDLE  ALT=\"y=250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The two speeds are y+25 = 275 km/h and y-25 = 225 km/h.<br><BR>\n" );
document.write( "ANSWER: the speed of the plane in still air is 275 km/h.<br><BR>\n" );
document.write( "e) 4950/275 = 18; 4950/225 = 22; total time 18+22 = 40 hours.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );