document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192602>Question 1192602</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In going over 750 kms, it takes a passenger plane 2 hour less time to fly with a tailwind of 50 kph than against a headwind travelling at the same speed. How fast was the passenger plane flying at each way of the course? </SPAN>\n" );
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document.write( "With the wording exactly as shown, the problem can't be answered, because we don't know the exact distance.  (The problem says the plane went OVER 750km; it doesn't say it went 750km.)<br><BR>\n" );
document.write( "Assuming the distance is in fact exactly 750km....<br><BR>\n" );
document.write( "The plane's speed one direction is its speed in still air plus the wind speed; in the other direction it is its speed in still air minus the wind speed.  Since the wind speed is 50km/h, the difference in the two speeds is 100km/h.<br><BR>\n" );
document.write( "If a formal algebraic solution is not required, the problem can be solved quickly by playing with numbers. 150*5=750, and 250*3=750; so 5 hours at 150km/h and 3 hours at 250km/h satisfy the given conditions.<br><BR>\n" );
document.write( "For a solution using formal algebra, I would let the two times in hours be x and x+2, so that the two speeds are 750/x and 750/(x+2).  Then I would write and solve an equation that says the difference in speeds at the two times is 100km/h -- literally, \"the speed for the shorter time is 100km/h more than the speed for the longer time\":<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%2Fx=750%2F%28x%2B2%29%2B100 ALIGN=MIDDLE  ALT=\"750%2Fx=750%2F%28x%2B2%29%2B100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%28x%2B2%29=750%28x%29%2B100%28x%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"750%28x%2B2%29=750%28x%29%2B100%28x%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750x%2B1500=750x%2B100x%5E2%2B200x ALIGN=MIDDLE  ALT=\"750x%2B1500=750x%2B100x%5E2%2B200x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100x%5E2%2B200x-1500=0 ALIGN=MIDDLE  ALT=\"100x%5E2%2B200x-1500=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%2B2x-15=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%28x-3%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%28x-3%29=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=-5 ALIGN=MIDDLE  ALT=\"x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The negative value for time of course makes no sense; so x=3 and x+2=5.<br><BR>\n" );
document.write( "The two speeds are then 750/3=250 and 750/5=150.<br><BR>\n" );
document.write( "ANSWERS: 250km/h with the wind; 150km/h against the wind<br><BR>\n" );
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