Pierre Suu/Getty; Daniele Venturelli/WireImage Kim Kardashian and Gwyneth Paltrow
The two stars both happen to use Oura Ring, a wearable device to track sleep, which they discovered after Kardashian West shared a screenshot of her app on her Instagram Story on Monday. The data showed that she had slept 8 hours and 15 minutes the night before, which the app considers "optimal."
Paltrow saw Kardashian West's story, and reposted it in disbelief.
"Okay WHAT?? I thought I was killing it at this @ouraring game… I guess not," the actress, 48, posted on her own Story.
"This is my lame ass score," she added, along with a screenshot her app showing that she got 7 hours and 17 minutes of sleep, earning her a "good" rating.
Kim Kardashian/Instagram Gwyneth Paltrow
Kardashian West, 40, responded on Tuesday, saying, "One thing about me… I can SLEEP!"
And that night she had upped the competition considerably, coming in with 9 hours and 36 minutes of sleep. Kardashian tagged Paltrow in her post, and said, "I'm just showing off now I know! LOL."
Kim Kardashian/Instagram Kim Kardashian West
Paltrow spoke to PEOPLE in 2017 about changing up her eating habits and adding supplements to her diet to manage her exhaustion.
"I thought, 'I eat well, I sleep, I exercise — so why am I always so tired? I don't get it,' " she said.
The mom of two said she reexamined her food choices to pick items that boost her energy.
"I think as I've gotten older and hopefully wiser I've tried to focus on doing little things throughout my week to bolster my strength and energy," she said. "I'm trying not to cave into sugar cravings and lots of white carbs all the time, because that's my kind of go-to; if I get tired in the afternoon I want pretzels, or I want Swiss cheese on a cracker or a baguette. I really love white carbs, which is not great for optimizing your health and your energy."
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Kardashian, meanwhile, will occasionally give in to her need for lots of sleep. In March, she jokingly called out her hairstylist after he shared a photo of the reality star passed out in the salon chair as he did her hair.
"I f---ing hate you!!! LOL You exhausted me!" Kardashian joked in the comments section of his Instagram post.