document.write( "Question 597434: A man walks 31 miles, partly at the rate of 2 miles per hour and the rest at the rate of 5 miles per hour. If he had walked at the rate of 5 miles per hour for the same time as he actually walked at the rate of 2 miles per hour, and vice versa, he would have covered 15 miles more than he did. How long did it take him to walk the 31 miles? \n" ); document.write( "
Algebra.Com's Answer #378234 by ankor@dixie-net.com(22740)\"\" \"About 
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A man walks 31 miles, partly at the rate of 2 miles per hour and the rest at the rate of 5 miles per hour.
\n" ); document.write( " If he had walked at the rate of 5 miles per hour for the same time as he actually walked at the rate of 2 miles per hour, and vice versa, he would have covered 15 miles more than he did.
\n" ); document.write( " How long did it take him to walk the 31 miles?
\n" ); document.write( ":
\n" ); document.write( "Let x = time walked at 2 mph originally
\n" ); document.write( "and
\n" ); document.write( "Let y = time walked at 5 mph originally
\n" ); document.write( ":
\n" ); document.write( "In the 2nd scenario, he would have walked, 31 + 15 = 46 mi
\n" ); document.write( ":
\n" ); document.write( "Write a distance equation for each scenario
\n" ); document.write( "2x + 5y = 31
\n" ); document.write( "and
\n" ); document.write( "5x + 2y = 46
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st equation by 2, multiply the 2nd equation by 5
\n" ); document.write( "25x + 10y = 230
\n" ); document.write( "4x + 10y = 62
\n" ); document.write( "----------------subtraction eliminates y, find x
\n" ); document.write( "21x = 168
\n" ); document.write( "x = 168/21
\n" ); document.write( "x = 8 hrs at 2 mph originally
\n" ); document.write( ";
\n" ); document.write( "Find the time at 5 mph
\n" ); document.write( "2(8) + 5y = 31
\n" ); document.write( "5y = 31 - 16
\n" ); document.write( "5y = 15
\n" ); document.write( "y = 15/3
\n" ); document.write( "y = 3 hrs at 5 mph originally
\n" ); document.write( "therefore
\n" ); document.write( "8 + 3 = 11 hrs to walk the 31 miles
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check our solutions in the 2nd equation
\n" ); document.write( "2(3) + 5(8) = 46 min \n" ); document.write( "
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