document.write( "Question 78921: 2 cars leave for a destination 48km away. Car B going at a speed of 64km/hr started 12 minutes ahead of Car A which goes at a speed of 100 km/hr. How long will it take Car A to overtake Car B? \n" ); document.write( "

Algebra.Com's Answer #56604 by Edwin McCravy(20062) $\"\"$ $\"About$

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2 cars leave for a destination 48km away. Car B going at a speed
\n" ); document.write( "of 64km/hr started 12 minutes ahead of Car A which goes at a
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document.write( "Let t = the time it takes A to overtake B \r\n" );
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document.write( "Make this chart\r\n" );
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document.write( "          DISTANCE | RATE |    TIME\r\n" );
document.write( "CAR A              |      |        \r\n" );
document.write( "CAR B              |      |         \r\n" );
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document.write( "Fill in t for CAR A's time to overtake CAR B.\r\n" );
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document.write( "          DISTANCE | RATE |    TIME\r\n" );
document.write( "CAR A              |      |       t\r\n" );
document.write( "CAR B              |      |         \r\n" );
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document.write( "Fill in their given rates of speed:\r\n" );
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document.write( "          DISTANCE | RATE |    TIME\r\n" );
document.write( "CAR A              |  100 |       t\r\n" );
document.write( "CAR B              |   64 |         \r\n" );
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document.write( "Since CAR B had already been going 12 minutes, \r\n" );
document.write( "CAR B's traveling time is 12 minutes longer than\r\n" );
document.write( "CAR A's.  12 minutes is 12/60 hour or 1/5 hour.\r\n" );
document.write( "So we add 1/5 hour to CAR A's x hours to get\r\n" );
document.write( "CAR B's time.  This is t + 1/5, so fill that in\r\n" );
document.write( "for CAR A's time:\r\n" );
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document.write( "          DISTANCE | RATE |    TIME\r\n" );
document.write( "CAR A              |  100 |       t\r\n" );
document.write( "CAR B              |   64 | t + 1/5\r\n" );
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document.write( "Now fill in the two distances by using DISTANCE = RATE(TIME)\r\n" );
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document.write( "          DISTANCE | RATE |    TIME\r\n" );
document.write( "CAR A         100x |  100 |       t\r\n" );
document.write( "CAR B  64(t + 1/5) |   64 | t + 1/5\r\n" );
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document.write( "          DISTANCE | RATE |    TIME\r\n" );
document.write( "CAR A         100x |  100 |       t\r\n" );
document.write( "CAR B  64(t + 1/5) |   64 | t + 1/5\r\n" );
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document.write( "They traveled the same distsnce to the point where CAR A\r\n" );
document.write( "catches up, so we set the distances equal to each other:\r\n" );
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document.write( "         100t = 64(t + 1/5) \r\n" );
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document.write( "         100t = 64t + 64/5\r\n" );
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document.write( "Clear of fractions by multiplying through by 5\r\n" );
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document.write( "         500t = 320t + 64\r\n" );
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document.write( "         180t = 64\r\n" );
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document.write( "            t = 64/180\r\n" );
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document.write( "            t = 16/45 hr or (16/45)(60 minutes) = \r\n" );
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document.write( "            t =  minutes or 21 minutes 20 seconds.  \r\n" );
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document.write( "Now the first piece of information\r\n" );
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document.write( ">>...2 cars leave for a destination 48km away...<<\r\n" );
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document.write( "was not used.  However since it tells us they \r\n" );
document.write( "are only going to travel for 48km, we must find \r\n" );
document.write( "out whether car B had already gotten to the \r\n" );
document.write( "destination before car A could catch up to it. \r\n" );
document.write( "So we must calculate their distance to see.  \r\n" );
document.write( "It's 100x and 100(16/45 hr) = 35 5/9 km, so yes \r\n" );
document.write( "car A did catch up to car B before it reached \r\n" );
document.write( "its destination of 48 km.\r\n" );
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document.write( "Edwin
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