document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190217>Question 1190217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car leaves a city 20 minutes after a truck leaves the same city. The truck is traveling at an average speed of 60kph and the car is traveling at an average speed of 80kph. How long will it take for the car to overtake the truck? </SPAN>\n" );
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document.write( "kph = kilometers per hour\r<BR>\n" );
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document.write( "60 kph = (60 km/1 hr)*(1 hr/60 min) = 1 km per min<BR>\n" );
document.write( "80 kph = (80 km/1 hr)*(1 hr/60 min) = 4/3 km per min<BR>\n" );
document.write( "Divide the kph value by 60 to convert to km per min.\r<BR>\n" );
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document.write( "In short,<BR>\n" );
document.write( "60 kph = 1 km per min<BR>\n" );
document.write( "80 kph = 4/3 km per min\r<BR>\n" );
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document.write( "x = amount of time, in minutes, the car has driven\r<BR>\n" );
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document.write( "The truck got a 20 minute head start, so it has traveled 20 minutes longer compared to x.<BR>\n" );
document.write( "x+20 = amount of time, in minutes, the truck has driven\r<BR>\n" );
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document.write( "The truck drives at a speed of 1 km per min, so it travels a distance of 1*(x+20) = x+20 kilometers<BR>\n" );
document.write( "Use the formula<BR>\n" );
document.write( "Distance = rate*time\r<BR>\n" );
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document.write( "Meanwhile, the car travels (4/3)x kilometers\r<BR>\n" );
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document.write( "Summary table so far<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Vehicle</TD><TD >Distance (km)</TD><TD >Rate (km per min)</TD><TD >Time (minutes)</TD></tr><tr><TD >Car</TD><TD >(4/3)x</TD><TD >4/3</TD><TD >x</TD></tr><tr><TD >Truck</TD><TD >x+20</TD><TD >1</TD><TD >x+20</TD></tr>\n" );
document.write( "</TABLE>The vehicles meet up when they have traveled the same distance.\r<BR>\n" );
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document.write( "Equate those two distance expressions and solve for x.<BR>\n" );
document.write( "Car's distance = Truck's distance<BR>\n" );
document.write( "(4/3)x = x+20<BR>\n" );
document.write( "4x = 3(x+20)<BR>\n" );
document.write( "4x = 3x+60<BR>\n" );
document.write( "4x-3x = 60<BR>\n" );
document.write( "x = 60<BR>\n" );
document.write( "This is the amount of time, in minutes, needed for the car to meet up with the truck. Shortly afterward the car overtakes the truck.<BR>\n" );
document.write( "Both vehicles travel 80 km when the two have met up.\r<BR>\n" );
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document.write( "Answer: <font color=red>1 hour</font><BR>\n" );
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