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 #841339 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841339\">put this solution on YOUR website!</A><BR><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?\r<BR>\n" );
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document.write( "Let x represent the average speed of the plane in still air<BR>\n" );
document.write( "One way distance  = 4950<BR>\n" );
document.write( "Time taken = 4950/x\r<BR>\n" );
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document.write( "From Dublin to Miami there was a tail wind since it took less  time<BR>\n" );
document.write( "So speed on return trip = 4950/(x+50)\r<BR>\n" );
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document.write( "Time Miami to Dublin  -Time  Dublin to miami  =4 hours\r<BR>\n" );
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document.write( "4950/x - 4950/(x+50)= 4\r<BR>\n" );
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document.write( "multiply  equation by x(x+50)\r<BR>\n" );
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document.write( "4950(x+50)-4950x = 4x(x+50)\r<BR>\n" );
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document.write( "4950x +247500-4950x = 4x^2+200x\r<BR>\n" );
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document.write( "4x^2+200x-247500=0\r<BR>\n" );
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document.write( "divide by 4<BR>\n" );
document.write( "x^2+50x-61875=0\r<BR>\n" );
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document.write( "Solve the quadratic equation by any method \r<BR>\n" );
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document.write( "x= 225  <BR>\n" );
document.write( "Miami to Dublin 225 mph<BR>\n" );
document.write( "Return trip speed = 225+50 = 175 mph\r<BR>\n" );
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document.write( "Time to Dublin + Time to Miami = total time\r<BR>\n" );
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document.write( "(4950/225) + (4950/275)  \r<BR>\n" );
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document.write( "22 hours +  18 hours =40 hours\r<BR>\n" );
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document.write( "Now you can answer the questions yourself\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );