Please help me to solve related rate problem

Question

Two people start from the same point. One walks east at 3 mi/h and the other walks northeast at 5 mi/h. How fast (in mi/h) is the distance between the people changing after 15 minutes? (Round the answer to three decimal places)

I tried this problem 5 times but I got the wrong answer. So I need help. I want to know the answer and the process.

Answer 1

Let x = distance travelled by the eastbound walker in t hours

Let y = distance travelled by the northeastbound walker in t hours

Let z = distance between the walkers in t hours

By the Law of Cosines, z² = x² + y² - 2xycos45°

So, z² = x² + y² - √2 xy

2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt) - √2 [ x(dy/dt) + y(dx/dt) ]

When t = 15 min = 1/4 hr, x = 3/4 mi and y = 5/4 mi

dx/dt = 3 amd dy/dt = 5

Find z and then solve for dz/dt.