document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207036>Question 1207036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train travels a certain journey and is supposed to arrive at midday. When its average speed is 40km/h, it arrives at 1 p.m. When its average speed is 48km/h, it arrives at 11 a.m. What is the length of the journey? </SPAN>\n" );
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document.write( "Let x be the number of hours the trip takes at 48km/hr.<br><BR>\n" );
document.write( "Then, since the arrival time at the lower speed is 2 hours later, x+2 is the number of hours it takes at 40km/hr.<br><BR>\n" );
document.write( "The distances at the two speeds are the same:<br><BR>\n" );
document.write( "48(x) = 40(x+2)<BR>\n" );
document.write( "48x = 40x+80<BR>\n" );
document.write( "8x = 80<BR>\n" );
document.write( "x = 10<br><BR>\n" );
document.write( "The trip at 48km/hr takes 10 hours, so the distance is 48*10 = 480km.<br><BR>\n" );
document.write( "ANSWER: 480km<br><BR>\n" );
document.write( "Here is a quick informal way to solve the problem mentally, if your mental math is good....<br><BR>\n" );
document.write( "The ratio of the two speeds, as a fraction, is 40/48.<br><BR>\n" );
document.write( "The distances are the same, so the ratio of the times is the same as the ratio of the speeds.<br><BR>\n" );
document.write( "Since the difference in the times is 2 hours, write the ratio 40/48 as an equivalent fraction in which the difference between the numerator and denominator is 2: 40/48 = 10/12.<br><BR>\n" );
document.write( "So the trip takes 12 hours at 40km/hr or 10 hours at 48km/hr, making the trip 480km.<br>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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