document.write( "Question 122110This question is from textbook Algebra: structure and method: Book 1
\n" ); document.write( ": Erica hiked up a mountain trail at 3 km/h and returned at 4 km/h. The entire trip took 5 hours and 10 minutes, including the 1/2 hour she spent resting. How long was the trail? PLEASE HELP!!!!!!! The answer is 8 km, but I don't know how to get there. HELP!!!!!!!!! \n" ); document.write( "

Algebra.Com's Answer #89654 by solver91311(24713) $\"\"$ $\"About$

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document.write( "Start with distance = rate times time, or .  We can safely presume\r\n" );
document.write( "that the distance up the hill is the same as the distance back down the hill.\r\n" );
document.write( "Let's say that  is the distance up or down the hill,  is the\r\n" );
document.write( "rate up the hill (given as 3 km/h),  is the rate down the hill (given\r\n" );
document.write( "as 4 km/h), and  and  are the times she took going up and\r\n" );
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document.write( "We know she rested for 30 minutes, so she spent 5 hrs 10 min minus 30 minutes\r\n" );
document.write( "or 4 hrs 40 min actually hiking.  4 hr 40 min is 4 and 2/3 or  hours.\r\n" );
document.write( "Since , we can say that \r\n" );
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document.write( "Using , we can say that the distance up the hill is ,\r\n" );
document.write( "and the distance downhill is , but since we have established that\r\n" );
document.write( ", we can substitute and write .\r\n" );
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document.write( "Now we have two different expressions for the same distance, so we can set\r\n" );
document.write( "them equal to each other:\r\n" );
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document.write( "Next, solve for \r\n" );
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document.write( "So the time to go uphill is  hour or 2 and 2/3 hour.\r\n" );
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document.write( "Since she travelled at 3 km/hr uphill,  km.\r\n" );
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document.write( "Check the answer\r\n" );
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document.write( "If the time uphill was 8/3, and the total time was 14/3, the time downhill\r\n" );
document.write( "must have been 6/3, or 2 hours.  2 hours times 4 km/hr equals 8 km.\r\n" );
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document.write( "Answer checks.\r\n" );
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