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
Answer:
the distance between them is changing at 25mph after 2 hours
