This is less optimization, more practice in implicit differentiation.

Set your origin at the water station. I assume he runs north from the water station and then turns the corner going east. Then after the runner has turned the corner his y-coordinate is always 200.

The distance formula gives:

Then we take the derivative with respect to time since we want the time rate of change of distance:

, then

In our case, the problem says:

So that gives us:

meters/second