WASHINGTON — In an age of long commutes, late sports practices, endless workdays and 24/7 television programming, the image of Mom hanging up her dish towel at 7 p.m. and declaring “the kitchen is closed” seems a quaint relic of an earlier era.

It also harks back to a thinner America. And that may be no coincidence.

A new study, conducted on mice, hints at an unexpected contributor to the nation’s epidemic of obesity — and, if later human studies bear it out, a possible way to have our cake and eat it too, with less risk of weight gain and the diseases that come with it.

Just eat your cake — or better yet, an apple — earlier. Then wait 16 hours, until breakfast the next morning, to eat again.

“We have to come up with something that is a simple alternative to calorie counting,” said Satchidananda Panda, a regulatory biologist at the Salk Institute in La Jolla, Calif., who led the study published online Thursday by the journal Cell Metabolism.

Panda and his team put groups of mice on different eating regimens for 100 days. Animals in two of the groups dined on high-fat, high-calorie chow. Half of them were allowed to eat whenever they wanted, and nibbled on and off throughout the night and day. The other mice had access to food only for eight hours at night, when they were most active.

In human terms, this would be rough: No ice cream while watching “Glee.” No second glass of wine while talking things over with the spouse. Not even a late-night glass of warm milk.