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

Answer:

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