You can use the phrase eat up any time you're talking about something — or someone — who uses up or consumes resources, especially at a rapid pace.
You might decide to buy a gas-electric hybrid car if you prefer a vehicle that doesn't eat up gasoline. Airplanes also eat up fuel, and an expensive hobby like skiing can quickly eat up all of your savings if you're not careful. Eat up can literally mean "eat everything" as well, like when your grandmother sings out, "Eat up!" as she serves you a big plate of her famous broccoli casserole.