“How comfortable would you feel if you had to take you hands off the wheel right now? Not very,” she said. “It is step by step process to get the consumer comfortable with that and understand it.”

Yet Barra may be underestimating just how ready the population really is for driverless technology, especially working moms. At a panel discussion on trends in technology at Fortune’s Most Powerful Women Summit in Laguna Niguel, Claire Hughes Johnson, the vice president of self-driving cars for Google [X](GOOG) , spoke about the latest developments in autonomous driving.

Like Barra, Johnson was cautious about how willing the audience of female executives would be to, say, put their children in a driverless car. “I myself am not ready,” said Johnson. Yet when the panel’s moderator, Fortune Senior Editor Michal Lev-Ram, asked the crowd who would put their kids in a driverless car today, a surprising thing happened.

A majority of the women raised their hands. Even the business leaders with their hands up were surprised by how large their “daring” cohort really was. But after a few moments, it became clear why so many women were willing to jump head first into driverless technology: time.

The average mom drives her children around for 1,248 miles per year, according to a 2013 study. That’s the equivalent of mothers spending two weeks of every year just getting their kids from A to Z. In 1995 (the last time The Surface Transportation Policy Project surveyed the driving habits of working moms), mothers spent more than half their time in the car chauffeuring their kids and doing errands. In the last twenty years, there is plenty of evidence that suggests that percentage has only increased.

While more mothers work today than ever before, the pressures of being the “Super Mom” who does everything from going to board meetings as well as ballet practices are increasing. The labor force participation rate for all mothers with children under 18 was 70% in 2013. Children with mothers who work — particularly during their early years — have been found to perform just as well in school as those with stay-at-home mothers, yet the phenomenon of “mom guilt” is still very much alive for many working mothers.

Eliminating the time moms (and dads for that matter) spend chauffeuring their kids around — which is generally not quality time to begin with — could give them more time to do other things with their children, and also get more work done.

“The way we think about a car will fundamentally change,” said Johnson. “That’s a lot of time and effort to move your children around.”

Time aside, the cost of owning a car could also decline after autonomous driving emerges from Google’s labs and hits the road. A car is typically the second most expensive item a household buys and costs an average of $9,000 annually to operate, says Johnson. Google claims autonomous driving could reduce accident-related expenses by at least $400 billion a year while reducing the number of cars on the road by 90% through more efficient sharing of vehicles.

The time and money savings combined could be a boon for working parents who already feel strapped by both.

“In 10 years it will be quite common, and one day we’ll think it was lunacy we ever let a human behind the wheel,” Silicon Valley venture capitalist Marc Andreessen said in a recent Fortune cover story.

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