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Trains A and B leave the same city at right angles at the same time.
\n" ); document.write( " Train B travels 5 mph faster than Train A.
\n" ); document.write( " After 2 hours, they are 50 miles apart. Find the speed of each train.
\n" ); document.write( ":
\n" ); document.write( "let s = speed of train A
\n" ); document.write( "then
\n" ); document.write( "(s+5) = speed of train B
\n" ); document.write( "After 2 hrs:
\n" ); document.write( "train A dist = 2s
\n" ); document.write( "train B dist = 2(s+5)
\n" ); document.write( ":
\n" ); document.write( "We can treat this as a pythag, problem where a^2 + b^2 = c^2
\n" ); document.write( "Where
\n" ); document.write( "a = 2s
\n" ); document.write( "b = 2(s+5)
\n" ); document.write( "c = 50
\n" ); document.write( ":
\n" ); document.write( "(2s)^2 + (2(s+5))^2 = 50^2
\n" ); document.write( "4s^2 + (2s + 10)^2 = 2500
\n" ); document.write( "4s^2 + 4s^2 + 40s + 100 = 250
\n" ); document.write( "A quadratic equation
\n" ); document.write( "8s^2 + 40s + 100 - 2500 = 0
\n" ); document.write( "8s^2 + 40s - 2400 = 0
\n" ); document.write( "Simplify divide by 8
\n" ); document.write( "s^2 + 5s - 300 = 0
\n" ); document.write( "This will factor to
\n" ); document.write( "(s+20)(s-15) = 0
\n" ); document.write( "the positive solution
\n" ); document.write( "s = 15 mph is Train A
\n" ); document.write( "and
\n" ); document.write( "15 + 5 = 20 mph is train B
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this on calc:
\n" ); document.write( "enter