document.write( "Question 1209421: Car A starts in Sacramento at 11am. It travels along a 400 mile route to Los Angeles at 60 mph. Car B starts from Los Angeles at noon and travels to Sacramento along the same route at 75 mph. The route goes past Fresno which is 150 miles along the route from Los Angeles. How far from Fresno are the cars when they meet? \n" ); document.write( "

Algebra.Com's Answer #848782 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "Car A starts in Sacramento at 11am. It travels along a 400 mile route to Los Angeles at 60 mph.
\n" ); document.write( "Car B starts from Los Angeles at noon and travels to Sacramento along the same route at 75 mph.
\n" ); document.write( "The route goes past Fresno which is 150 miles along the route from Los Angeles.
\n" ); document.write( "How far from Fresno are the cars when they meet?
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document.write( "Let \"t\" be the time (in hours) for car A moving from S to LA to get the meeting moment.\r\n" );
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document.write( "Then the time for car B moving from LA to S is (t-1) hours to get the meeting point (one hour less).\r\n" );
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document.write( "The time equation for the meeting moment t is\r\n" );
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document.write( "    60t + 75*(t-1) = 400  miles  (the whole route length).\r\n" );
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document.write( "Simplify and find t from this equation\r\n" );
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document.write( "    60t + 75t - 75 = 400\r\n" );
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document.write( "    60t + 75t = 400 + 75\r\n" );
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document.write( "       135t   =    475\r\n" );
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document.write( "          t   =    475/135 = 3.518519  hours.\r\n" );
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document.write( "So, the time for the car B moving from LA to the meeting point is one hour less than that, i.e. 2.518519 hours.\r\n" );
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document.write( "The distance from LA to the meeting point is  75*2.518519 = 188.888925 miles.\r\n" );
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document.write( "It is 188.888925 -150 miles = 38.888925 miles from Fresno, between Fresno and Sacramento.\r\n" );
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document.write( "ANSWER.  The meeting point is 38.9 miles from Fresno, between Fresno and Sacramento.\r\n" );
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