In a tug-of-war between two athletes, each pulls on the rope with a force of 190 N. What is the tension in the rope?

The same.

It's just 909 N in the opposite direction for each person. If this force against the ground (usually called the force of Friction or Fs) was not there they would not be able to put the tension upon the rope.

To calculate the tension in the rope during a tug-of-war, you add up the forces applied by both athletes. In this case, each athlete pulls with a force of 190 N. Since there are two athletes, you simply add their forces together:

Tension in the rope = Force athlete 1 + Force athlete 2

Tension in the rope = 190 N + 190 N

Tension in the rope = 380 N

Therefore, the tension in the rope during the tug-of-war is 380 N.