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Two cruise ships leave port at the same time.
\n" ); document.write( "One heads south and the other goes east.
\n" ); document.write( " Later that day they are 170 miles apart.
\n" ); document.write( " One ship has traveled 70 miles more than the other ship.
\n" ); document.write( " How many miles has each ship gone?
\n" ); document.write( ":
\n" ); document.write( "Time is not a factor here, so the dist formula is not used.
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\n" ); document.write( "Let x = the distance traveled by the 1st ship
\n" ); document.write( "then
\n" ); document.write( "(x+70) = the distance traveled by 2nd ship
\n" ); document.write( ":
\n" ); document.write( "This a right angle problem where a^2 + b^2 = c^2:
\n" ); document.write( "one leg (a) = x
\n" ); document.write( "2nd leg (b) = (x+70)
\n" ); document.write( "hypotenuse (c) = dist between the ships (170mi)
\n" ); document.write( ":
\n" ); document.write( "x^2 + (x+70)^2 = 170^2
\n" ); document.write( "x^2 + x^2 + 140x + 4900 = 28900
\n" ); document.write( "2x^2 + 140x + 4900 - 28900 = 0
\n" ); document.write( "2x^2 + 140x - 24000 = 0
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "x^2 + 70x - 12000 = 0
\n" ); document.write( "You can use the quadratic formula a=1, b=70, c=-12000, but it will factor to
\n" ); document.write( "(x+150)(x-80) = 0
\n" ); document.write( "the positive solution
\n" ); document.write( "x = 80 mi traveled by the 1st ship
\n" ); document.write( "then
\n" ); document.write( "80 + 70 = 150 mi traveled by the 2nd ship
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this on your calc; enter: