Rhodey is aware of Tony's relationship with food and sleep ever since they became friends at MIT. Tony would get so lost into a project that he'd ignore 'minor' details like sleeping and eating. The only thing keeping him hydrated would be coffee on such occasions. On more than one occasion Tony had crashed pretty hard after one of his binges. So, Rhodey had learned early on how to handle Tony in such situations. Bribing him with coffee as an incentive won't work as he'd already be overloaded with caffeine as it is, so, Rhodey had come up with his own way of keeping his best friend in the land of living - namely bribing him with his favorite food and if that didn't work, threatening him always did the trick for him.
Jarvis informs Colonel Rhodes of his friend's situation and Rhodey walks into the lab holding a tray of food.
"Hey Tony, I brought you some food." Rhodey says.
"Sorry honey-bear but I'm a bit busy now." Tony answers distractedly, not even looking up from his work.
"Ah.. but it's burgers from your favorite place." That gets Tony's attention. "Also there are milkshakes." Rhodey adds enticingly.
"Well... " Tony says wavering.
Bait set, time to reel him in.
"And if you don't... I'll let Justin Hammer upgrade the War Machine." Rhodey says with all the seriousness that he could muster.
The speed with which Tony's head shot up was almost comical. The glare he shot Rhodey wasn't.
"You wouldn't." Tony said, still throwing a death glare towards him.
"Try me." Rhodey replied in all seriousnes and handed Tony the tray of food.
Tony grudgingly accepted the tray and dug into his favourite food with gusto while still grumbling about manipulative best friends and cursing Hammer between bites of his burger.
Rhodey left the lab then, a huge smile on his face, trusting the genius to handle things from there on.
Knowing Tony the longest sometimes had it's perks.
Mission Accomplished.
TBC