document.write( "Question 65498This question is from textbook Essential Algebra
\n" ); document.write( ": Abigail Nightwind has planned a bike trip with some friends from her village. They will bike for 8 hours, then hike for 4 hours. If they can bike on the average 10mph fater than they can hike and if they will cover a total of 122 miles, how fast can Abigail and her friends bike? \n" ); document.write( "
Algebra.Com's Answer #46044 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Abigail Nightwind has planned a bike trip with \r\n" );
document.write( "some friends from her village. They will bike \r\n" );
document.write( "for 8 hours, then hike for 4 hours. If they \r\n" );
document.write( "can bike on the average 10mph fater than they \r\n" );
document.write( "can hike and if they will cover a total of 122 \r\n" );
document.write( "miles, how fast can Abigail and her friends\r\n" );
document.write( "bike?\r\n" );
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document.write( "Funmath above let the unknown represent\r\n" );
document.write( "the hiking rate.  To be a little different,\r\n" );
document.write( "I'm going to let the unknown represent the\r\n" );
document.write( "biking rate instead.  After all that's what\r\n" );
document.write( "we're asked for in the question.  I also\r\n" );
document.write( "think it makes it easier to see if you use\r\n" );
document.write( "a DRT chart.\r\n" );
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document.write( "Let x = the biking rate.\r\n" );
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document.write( "Make this DRT-chart\r\n" );
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document.write( "             D        R     T\r\n" );
document.write( "biking                         \r\n" );
document.write( "hiking   \r\n" );
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document.write( "and fill in x for the biking rate:\r\n" );
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document.write( "             D        R     T\r\n" );
document.write( "biking                x      \r\n" );
document.write( "hiking                                             \r\n" );
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document.write( ">>...They can bike on the average 10mph faster\r\n" );
document.write( "than they can hike...<<\r\n" );
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document.write( "This means that they can hike on the average\r\n" );
document.write( "10mph slower than they can bike. So their hiking\r\n" );
document.write( "rate is 10mph slower or x-10. So fill that in\r\n" );
document.write( "for the hiking rate \r\n" );
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document.write( "             D        R     T\r\n" );
document.write( "biking                x      \r\n" );
document.write( "hiking               x-10    \r\n" );
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document.write( ">>..They will bike for 8 hours, then hike for \r\n" );
document.write( "4 hours...<<\r\n" );
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document.write( "So fill in 8 for the biking time, and 4 for\r\n" );
document.write( "the hiking time: \r\n" );
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document.write( "             D        R     T\r\n" );
document.write( "biking                x     8\r\n" );
document.write( "hiking               x-10   4\r\n" );
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document.write( "Now we fill in the distances using D = RT\r\n" );
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document.write( "             D        R     T\r\n" );
document.write( "biking      8x        x     8\r\n" );
document.write( "hiking    4(x-10)    x-10   4\r\n" );
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document.write( "Now that the chart is filled in, we return\r\n" );
document.write( "to the word problem to see what we have not \r\n" );
document.write( "used in filling in the chart.  It is these\r\n" );
document.write( "words:\r\n" );
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document.write( ">>...They will cover a total of 122 miles...<<\r\n" );
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document.write( "So,\r\n" );
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document.write( "distance biking + distance hiking = 122 miles\r\n" );
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document.write( "             8x + 4(x-10) = 122\r\n" );
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document.write( "             8x + 4x - 40 = 122\r\n" );
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document.write( "                 12x - 40 = 122\r\n" );
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document.write( "                      12x = 162\r\n" );
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document.write( "                        x = 162/12\r\n" );
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document.write( "                        x = 27/2\r\n" );
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document.write( "                        x = 13.5 mph\r\n" );
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document.write( "Checking: They bike at 13.5mph and hike at 3.5mph\r\n" );
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document.write( "They bike at 13.5mph for 8 hours and that's a distance\r\n" );
document.write( "of 108 miles they bike.\r\n" );
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document.write( "They hike at 3.5mph for 4 hours and that's a distance\r\n" );
document.write( "of 14 miles they hike.\r\n" );
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document.write( "108 miles biked + 14 miles hiked = 122 miles total.\r\n" );
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document.write( "Edwin
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