No need to play around with adding keyframes.
Add a path to the scene, select the Particle and in the Modify panel click on "Pick Path" and then on the Path in the scene.

Next scrub along the Timeline to the point where you wish to have the Particle complete the Path route. In the "Position" field enter 100.

The Particle will now follow the Path for the time duration selected.
If you want the Particle to move faster then move the last keyframe to the left on the Timeline. Moving the last keyframe to the right will make the Particle move slower.
Gerry
System: Win 10 Pro (21H2), Asus X99-E WS, CPU i7-5930K -3,5 GHz, 32 GB DDR4 2666-16 RAM, NVidia GTX 1080 Ti GPU - 11 GB VRAM(Driver Studio-536.99), Samsung 850 Pro 512 GB SSD, 6 TB HD storage.