Correct way to set up this Laravel relationship?

I'm after a bit of logic advice. I am creating a system where users login and register their participation at an activity. They can participate at an activity many times. What is the best way to do this? I want to ensure I can use eloquent with this rather than creating my own functions.

I am imagining...

Users:

id

Activitys:

id
name

Participations:

id
user_id
activity_id
time_at_activity

I want to later be able to do such things as: $user->participations->where('activity_id', 3) for example.

What is the best way to set this up? I had in mind..

User: hasMany->Participations

Activity: belongsTo->Participation

Participation: hasMany->Activitys & belongsTo->User

Does this look correct?

via Chebli Mohamed