document.write( "Question 272228: Two runners start from the same point at the same time. They will be 4 miles apart at the end of two hours if running in the same direction, and they will be 16 miles apart at the end of one hour if running in opposite directions. Find their speeds. \n" ); document.write( "
Algebra.Com's Answer #199233 by ankor@dixie-net.com(22740)\"\" \"About 
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Two runners start from the same point at the same time.
\n" ); document.write( " They will be 4 miles apart at the end of two hours if running in the same direction,
\n" ); document.write( " and they will be 16 miles apart at the end of one hour if running in opposite directions.
\n" ); document.write( "Find their speeds.
\n" ); document.write( ":
\n" ); document.write( "Let x = speed of the faster runner
\n" ); document.write( "Let y = speed of the slower
\n" ); document.write( ":
\n" ); document.write( "Write a distance equation for each scenario
\n" ); document.write( ":
\n" ); document.write( "2(x - y) = 4; running the same direction
\n" ); document.write( "simplify, divide by 2
\n" ); document.write( "x - y = 2
\n" ); document.write( "and
\n" ); document.write( "1(x + y) = 16; running opposite directions
\n" ); document.write( ":
\n" ); document.write( "Add the two equations
\n" ); document.write( "x - y = 2
\n" ); document.write( "x + y = 16
\n" ); document.write( "-------------addition eliminates y, find x
\n" ); document.write( "2x = 18
\n" ); document.write( "x = 9 mph is the faster runner
\n" ); document.write( "then
\n" ); document.write( "9 + y = 16
\n" ); document.write( "y = 16 - 9
\n" ); document.write( "y = 7 mph is the slower runner
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution in the two equations
\n" ); document.write( "2(9 - 7) = 4
\n" ); document.write( "and
\n" ); document.write( "1(9 + 6) = 16
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