Problem Solving

Nicky and Cristina are running a 1000 meter race. Since Cristina is faster than Nicky, she gives a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?

This is a chase problem where people are moving in the same direction.

When setting up the equations:

Christina: 5 m/s * t
Nicky: 3 m/s * (t+12)

If Nicky is slower and gets the headstart why would we list Nicky to have t + 12? wouldn't be the other way around where Nicky gets 3t and Christina would be 12 seconds after as 5(t+12)?

Thanks.