To Keep Up With

[Bobbert]

Do my sentences below convey the meaning of:

“To keep up with” (to not fall behind);
“To keep up with” (to be as good as someone else/to be able to do the same things as someone else)?

If the verb constructions I chose are not correct, what other verb constructions should I have used? Seguir el ritmo/paso de? Seguirle el ritmo/paso a? Mantenerse a la altura con? Mantenerse al nivel de?

These are my attempts:

To Keep Up With (To Not Fall Behind)
I often miss my Spanish class and that makes it hard to keep up with my studies.
A menudo falto a mi clase de español y eso hace que sea difícil mantenerme el ritmo con mis estudios.

We have to keep up with the orders; we cannot afford to get behind.
Tenemos que seguir el ritmo con los pedidos; no podemos darnos el lujo de quedarnos atrás.

I’m hoping to be able to keep up with my chores today.
Tengo esperanzas de poder seguir el ritmo de mis quehaceres hoy.

To Keep Up With (To Be As Good As Someone Else/To Be Able To Do The Same Things As Someone Else)
Don't even think about keeping up with your colleagues if you're not going to deliver the reports on time.
Ni se te ocurra mantenerte a la par con tus colegas si no vas a entregar los informes a tiempo.

Why do you try to keep up with Gloria? She comes from a wealthy family and has plenty of disposible income.
¿Porque intentas mantenerte a la par con Gloria? Viene de una familia adinerada y tiene un montón de ingresos disponibles.

I appreciate any and all input you can give me.