document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132034>Question 1132034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An airplane travels west at 180 km/h, and returns east with the jet stream at 300 km/h. What was the average speed in km/h for the whole trip? </SPAN>\n" );
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document.write( "Let d be the distance for each leg of the trip.  Then the total time for the trip is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F180%2Bd%2F300+=+%28300d%2B180d%29%2F%28180%2A300%29+=+%28%28300%2B180%29d%29%2F%28180%2A300%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The total distance is 2d; the average speed is total distance divided by total time:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2d%2F%28%28%28300%2B180%29d%29%2F%28180%2A300%29%29+=+%28%282d%28180%2A300%29%29%2F%28%28300%2B180%29d%29%29+=+%282%28180%2A300%29%29%2F%28300%2B180%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Simplified, that is 225 km/h.<br><BR>\n" );
document.write( "Note the expression could have been simplified along the way; I kept it in this form so you could see where the formula cited by the other tutor came from.<br><BR>\n" );
document.write( "ANSWER: the average speed is 225 km/h.<br><BR>\n" );
document.write( "======================================================<br><BR>\n" );
document.write( "Here is a different way I like to use for solving a problem like this.<br><BR>\n" );
document.write( "The ratio of the two speeds is 180:300 = 3:5.  Since the distances are the same, that means the ratio of the times is 5:3.<br><BR>\n" );
document.write( "So for 5/8 of the time the plane is flying at 180 km/h, and for 3/8 of the time it is flying at 300 km/h.  The average speed is then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F8%29%28180%29%2B%283%2F8%29%28300%29+=+900%2F8+%2B+900%2F8+=+900%2F4+=+225 ALIGN=MIDDLE  ALT=\"%285%2F8%29%28180%29%2B%283%2F8%29%28300%29+=+900%2F8+%2B+900%2F8+=+900%2F4+=+225\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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