How does distance from the epicenter affect the s-p time interval

Farther from the epicenter, the s - p time interval is longer.

Explanation:

Both waves are seismic waves, that means, both of them could pass energy from one place to another.

The P waves (primary), since they can travel faster, they arrive first from the epicenter to the place of impact, it can travel trough solids or liquids.

The s waves (secondary), they are slower, they can only travel by solids.

So by passing the time of the Earthquake, the P wave will traveling faster from the epicenter to the outside part, and the S wave will take more time, so like in a marathon, the master wave (P) will reach the target first.

Hope this info is useful.