document.write( "Question 1207498: Two cities, A and B, are connected by means of a highway 150 kms long. An automobile leaves A at
\n" ); document.write( "1:00 pm and travels at a uniform rate of 40 kms per hour toward B. Thirty minutes later, another
\n" ); document.write( "automobile leaves city A and travels toward B at a uniform rate 55 kms per hour. At what time will
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Algebra.Com's Answer #845414 by ikleyn(52787)\"\" \"About 
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\n" ); document.write( "Two cities, A and B, are connected by means of a highway 150 kms long. An automobile leaves A at
\n" ); document.write( "1:00 pm and travels at a uniform rate of 40 kms per hour toward B. Thirty minutes later, another
\n" ); document.write( "automobile leaves city A and travels toward B at a uniform rate 55 kms per hour. At what time will
\n" ); document.write( "the second car overtake the first car?
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document.write( "Let t be the time after 1:00 pm, in hours.\r\n" );
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document.write( "The distance traveled by first auto is 40t kilometers.\r\n" );
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document.write( "The distance traveled by the second auto is 55*(t-0.5) kilometers.\r\n" );
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document.write( "We want to find t when the distance is the same (overtake condition)\r\n" );
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document.write( "    40t = 55(t-0.5).\r\n" );
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document.write( "Simplify this equation and find t\r\n" );
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document.write( "    40t = 55t - 0.5*55\r\n" );
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document.write( "     0.5*55 = 55t - 40t\r\n" );
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document.write( "     27.5 = 15t\r\n" );
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document.write( "     t = 27.5/15 = 55/30 = 110/60 = 1 hour and 50 minutes.\r\n" );
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document.write( "The second auto will overtake the first at 1 hour and 50 minutes after 1:00 pm, which is 2:50 pm.\r\n" );
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document.write( "The traveled distance is less than 40 km/h * 2 hours = 80 kilometers;\r\n" );
document.write( "hence, the second car overtakes the first one before than either car will get the city B.\r\n" );
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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( "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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