Two boats leave a port at the same time. one travels west at 20 mph, and the other travels south at 15 mph. how fast is the distance between them changing after 2 hours?

Let's define variables:
 x: boat travels west
 y: boat travels south
 d: distance between boats.
 Using the Pythagorean theorem we have:
 d ^ 2 = x ^ 2 + y ^ 2
 Where,
 x = 20 * 2 = 40 miles
 y = 15 * 2 = 30 miles
 d = root ((40) ^ 2 + (30) ^ 2) = 50 miles
 We now derive the equation with respect to time:
 2dd '= 2xx' + 2yy '
 We cleared d ':
 d '= (2xx' + 2yy ') / (2d)
 Substituting values:
 d '= (2 * (40) * (20) + 2 * (30) * (15)) / (2 * (50))
 d '= 25 mph
 
 the distance between them is changing at 25mph after 2 hours

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