document.write( "Question 1190217: 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? \n" ); document.write( "

Algebra.Com's Answer #821813 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "A car leaves a city 20 minutes after a truck leaves the same city.
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A quick and short \"naive\" solution

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document.write( "In 20 minutes, a truck is   = 20 km ahead the car.\r\n" );
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document.write( "Moving faster than the truck, the car has approaching speed of 80-60 = 20 km/h.\r\n" );
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document.write( "Therefore, it is clear that the car will overtake the truck in  = 1 hour.    ANSWER\r\n" );
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A slow Algebra solution

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document.write( "Let t be the time after the car started.\r\n" );
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document.write( "So, to the catching moment, the car moves t hours.\r\n" );
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document.write( "The truck started 20 minutes earlier, so the truck moved (t+1/3) hours till the car catches up the truck.\r\n" );
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document.write( "They cover the same distance, so we write this distance equation\r\n" );
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document.write( "    80*t = 60*(t+1/3)\r\n" );
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document.write( "Left side is the distance covered by the car; right side is the distance covered by the truck.\r\n" );
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document.write( "To solve, multiply both sides of the equation by 3. You will get\r\n" );
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document.write( "    240t = 60*(3t+1)\r\n" );
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document.write( "Simplify and find t\r\n" );
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document.write( "    240t = 180t + 60\r\n" );
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document.write( "    240t - 180t = 60\r\n" );
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document.write( "        60t     = 60\r\n" );
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document.write( "          t     = 60/60 = 1  hour.\r\n" );
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document.write( "So, the car overtakes the truck in 1 hour after the car' start.\r\n" );
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document.write( "You get the same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved (in two different ways for your better understanding).\r
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\n" ); document.write( "\n" ); document.write( "For simple Travel & Distance problems, see introductory lessons \r
\n" ); document.write( "\n" ); document.write( "    - Travel and Distance problems \r
\n" ); document.write( "\n" ); document.write( "    - Travel and Distance problems for two bodies moving in opposite directions \r
\n" ); document.write( "\n" ); document.write( "    - Travel and Distance problems for two bodies moving in the same direction (catching up)\r
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\n" ); document.write( "\n" ); document.write( "They are written specially for you.\r
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\n" ); document.write( "\n" ); document.write( "You will find the solutions of many similar problems there.\r
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\n" ); document.write( "\n" ); document.write( "Read them and learn once and for all from these lessons on how to solve simple Travel and Distance problems.\r
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\n" ); document.write( "\n" ); document.write( "Become an expert in this area.\r
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