document.write( "Question 356064: can you please help me with this mind breaking question...and thank you for
\n" ); document.write( "advance:). A traveler left a town A at 5:00 a.m. and traveled toward a town B.
\n" ); document.write( "At 7:00 a.m. another traveler left town B and traveled toward A. They met at
\n" ); document.write( "9:05a.m. The first traveler arrived at B and the second arrived at A at the
\n" ); document.write( "same time. How long did each travel? \n" ); document.write( "

Algebra.Com's Answer #254214 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Let the 1st traveler's rate be x mph\r\n" );
document.write( "Let the 2nd traveler's rate be y mph\r\n" );
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document.write( "Let's take a look at the moment when they met, which was 9:05.\r\n" );
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document.write( "At 9:05 the 1st traveler, who started at 5AM, had been traveling for\r\n" );
document.write( "4 hours and 5 minutes, or  hours or  hours or  hours.  \r\n" );
document.write( "At rate x mph, he had traveled  or  miles.\r\n" );
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document.write( "At 9:05 the 2nd traveler, who started at 7AM, had been traveling for\r\n" );
document.write( "2 hours and 5 minutes, or  hours or  hours or  hours.  \r\n" );
document.write( "At rate y mph, he had traveled  or  miles. \r\n" );
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document.write( "When they met at 9:05, each had the same number of miles yet to go that \r\n" );
document.write( "the other had already been.  That is, the 1st traveler had \r\n" );
document.write( "miles yet to go and the 2nd traveler had  miles yet to go.\r\n" );
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document.write( "We are told that they arrived at the same time.  So we will calculate each\r\n" );
document.write( "traveler's time after 9:05 and set them equal. \r\n" );
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document.write( "Since , the 1st traveler's time was his distance yet\r\n" );
document.write( "to go, , divided by his rate x, or  or  or  hours till he \r\n" );
document.write( "reached town B.\r\n" );
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document.write( "Also the 2nd traveler's time was his distance yet to go, , divided\r\n" );
document.write( "by his rate y, or  or  or  hours till he reached town A.\r\n" );
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document.write( "Since they arrived at their respective destinations at the same time, we set\r\n" );
document.write( "these times equal:\r\n" );
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document.write( "     \r\n" );
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document.write( "Multiplying both sides by 12 eliminates the 12's from the denominators:\r\n" );
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document.write( "     \r\n" );
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document.write( "Cross multiplying:\r\n" );
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document.write( "     \r\n" );
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document.write( "Taking positive square roots of both sides\r\n" );
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document.write( "            \r\n" );
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document.write( "Dividing both sides by 5x\r\n" );
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document.write( "The 1st traveler's time to reach his destination after 9:05 was\r\n" );
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document.write( " which equals  which equals \r\n" );
document.write( "      \r\n" );
document.write( " or 2 hours and 55 minutes after 9:05.\r\n" );
document.write( "So the 1st traveler reached his destination at 12 noon.\r\n" );
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document.write( "It isn't necessary, but, as a check, let's see if the 2nd traveler also reached\r\n" );
document.write( "his destination at 12 noon.\r\n" );
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document.write( "The 2nd traveler's time to reach his destination after 9:05 was\r\n" );
document.write( "\r\n" );
document.write( " which equals  which equals \r\n" );
document.write( "      \r\n" );
document.write( " or 2 hours and 55 minutes after 9:05.\r\n" );
document.write( "So the 2nd traveler also reached his destination at 12 noon.\r\n" );
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document.write( "So the 1st traveler started at 5AM and arrived at noon, so his time was 7 hours.\r\n" );
document.write( "The 2nd traveler started at 7AM and arrived at noon, so his time was 5 hours.\r\n" );
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document.write( "[Notice that this problem is independent of their speeds and the distance they\r\n" );
document.write( "traveled.]\r\n" );
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document.write( "Edwin

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