document.write( "Question 618836: Derick and Peter walk from point Y and Z, respectively walks toward each other at the same in constant speed. They meet the first time at a point that is eight miles away from Point Y. They kept going without stop. As soon as one reach Y or Z, one returns in the same route. They meet the second time at a point five miles away from point Z. What is the distance between the two points that they met one another? \n" ); document.write( "
Algebra.Com's Answer #389169 by ankor@dixie-net.com(22740)\"\" \"About 
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Derick and Peter walk from point Y and Z, respectively walks toward each other at the same in constant speed.
\n" ); document.write( " They meet the first time at a point that is eight miles away from Point Y.
\n" ); document.write( " They kept going without stop. As soon as one reach Y or Z, one returns in the same route.
\n" ); document.write( "They meet the second time at a point five miles away from point Z.
\n" ); document.write( " What is the distance between the two points that they met one another?
\n" ); document.write( ":
\n" ); document.write( "y------------>8mi------5mi<--------z
\n" ); document.write( ":
\n" ); document.write( "Let d = distance from y to z
\n" ); document.write( ":
\n" ); document.write( "First meeting:
\n" ); document.write( "D walks 8 mi
\n" ); document.write( "P walks (d-8) mi
\n" ); document.write( ":
\n" ); document.write( "2nd meeting:
\n" ); document.write( "D walks: (d-8) + 5 = d-3 mi
\n" ); document.write( "P walks: 8 + (d-5) = d+3 mi
\n" ); document.write( ":
\n" ); document.write( "The relationship of the distances walked by the two boys is the same for each meeting.
\n" ); document.write( "therefore
\n" ); document.write( "\"8%2F%28%28d-8%29%29\" = \"%28%28d-3%29%29%2F%28%28d%2B3%29%29\"
\n" ); document.write( "cross multiply
\n" ); document.write( "8(d+3) = (d-8)(d-3)
\n" ); document.write( "FOIL the right side
\n" ); document.write( "8d + 24 = d^2 - 3d - 8d + 24
\n" ); document.write( "Combine like terms on the right
\n" ); document.write( "0 = d^2 - 11d - 8d + 24 - 24
\n" ); document.write( "leaving
\n" ); document.write( "d^2 - 19d = 0
\n" ); document.write( "Factor
\n" ); document.write( "d(d-19) = 0
\n" ); document.write( "our solution
\n" ); document.write( "d = 19 mi from y to z
\n" ); document.write( ":
\n" ); document.write( "\"What is the distance between the two points that they met one another?\"
\n" ); document.write( "Assume this means how far from the 8mi from y to 5mi from z
\n" ); document.write( "(19-5) - 8 = 6 mi between the two points \n" ); document.write( "
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