document.write( "Question 1164293: amanda drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Amanda drove home, there was no traffic and the trip only took 5 hours. If her average rate was 18 miles per hour faster on the trip home, how far away does Amanda live from the mountains? \n" ); document.write( "
Algebra.Com's Answer #788608 by Theo(13342)\"\" \"About 
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r * t = d
\n" ); document.write( "r = rate
\n" ); document.write( "t = time
\n" ); document.write( "d = distance
\n" ); document.write( "going there, the formula becomes r * 7 = d
\n" ); document.write( "going home, the formula becomes r * 5 = d
\n" ); document.write( "her average rate going home was 18 miles per hour faster than her average rate going home.
\n" ); document.write( "going there, the formula stays at r * 7 = d
\n" ); document.write( "coming home, the formula becomes (r + 18) * 5 = d
\n" ); document.write( "simplify both formulas to get:
\n" ); document.write( "7r = d
\n" ); document.write( "5r + 90 = d
\n" ); document.write( "subtract the second equation from the first to get:
\n" ); document.write( "2r - 90 = 0
\n" ); document.write( "add 90 to both sides of that equation to get:
\n" ); document.write( "2r = 90
\n" ); document.write( "solve for r to get:
\n" ); document.write( "r = 45
\n" ); document.write( "7r = d becomes 7 * 45 = d which gets you d = 315
\n" ); document.write( "5r + 90 = d gets you 5 * 45 + 90 = d which gets you d = 315
\n" ); document.write( "the distance is 315 miles.
\n" ); document.write( "it takes her 7 hours at 45 miles per hour to get there.
\n" ); document.write( "it takes her 5 hours at 63 miles per hour to get home.
\n" ); document.write( "7 * 45 = 315 miles getting there.
\n" ); document.write( "5 * 63 = 315 miles going home.
\n" ); document.write( "she lives 315 miles from the mountains.\r
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