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rate * time = distance
\n" ); document.write( "train A travels 16 mph slower than train B. if rate of train A is x miles per hour, then rate of train B is (x+16) miles per hour.
\n" ); document.write( "let T = time in hours,
\n" ); document.write( "if A travels 220 miles in T hours, then x*T = 220.
\n" ); document.write( "if B travels 300 miles in T hours, then (x+16)*T = 300.
\n" ); document.write( "solving for T, we get
\n" ); document.write( "T = 220/x from the first equation, and
\n" ); document.write( "T = 300/(x+16) from the second equation.
\n" ); document.write( "since both equations equal T, they must be equal to each other, so
\n" ); document.write( "220/x = 300/(x+16)
\n" ); document.write( "solving for x, we multiply both sides of the equation by x*(x+16) to remove the denominators. equation becomes
\n" ); document.write( "220*(x+16) = 300*x
\n" ); document.write( "this becomes
\n" ); document.write( "220*x + 220*16 = 300*x
\n" ); document.write( "subtracting 220*x from both sides of the equations gets
\n" ); document.write( "220*16 = 300*x - 220*x
\n" ); document.write( "this becomes
\n" ); document.write( "3520 = 80*x
\n" ); document.write( "which becomes
\n" ); document.write( "x = 44 mph
\n" ); document.write( "it looks like train A is traveling 44 mph and train B is traveling 60 mph.
\n" ); document.write( "once we know this we can solve for T.
\n" ); document.write( "for train A, T = 220/44 = 5 hours
\n" ); document.write( "for train B, T = 300/60 = 5 hours
\n" ); document.write( "60 mph minus 44 mph = 16 mph so train B is traveling 16 mph faster than train A.
\n" ); document.write( "answer checks out, so answer is:
\n" ); document.write( "train A is traveling at 44 mph.
\n" ); document.write( "train B is traveling at 16 mph.\r
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