SEATTLE — Steve Case, AOL co-founder, said he invested an undisclosed amount in the Seattle-based company Flexcar through his $500 million Revolution LLC investment fund, which focuses on lifestyle, health, and resort businesses. Former Chrysler Chief Executive Lee Iacocca also will invest and join the board, Case said Aug. 30 in a phone interview with Bloomberg News. Retail gasoline prices have gained 35 percent in the past year, helping car-sharing services catch on in U.S. cities including Seattle, Washington, D.C., and Los Angeles. Flexcar and its Boston-based rival, Zipcar Inc., both say they’re signing twice as many members as a year ago; Zipcar claims 45,000 members, while Flexcar says it has 35,000. Car-share customers pay a fee to rent vehicles for as little as a half-hour. The cars are parked in neighborhoods or near a transit hub. Users reserve vehicles online or by phone, and use electronic cards to access them. They must then return the cars to reserved spots. Case, 47, said he became interested in Flexcar four months ago while walking past one of its parking spots near Revolution’s offices in Washington. He used the service several times to reach meetings around the city. Case’s investment will help Flexcar expand, according to the CEO of the six-year-old company, Lance Ayrault. Within five years, Flexcar expects to have 1 million members and a fleet of 20,000 cars, up from 450 today. About 25 percent of Flexcar’s members are businesses, including Seattle-based Starbucks Corp. and law firm Perkins Coie LLP, which isn’t replacing some cars in its motor pool. According to Bloomberg News, Flexcar’s customers in Seattle pay an hourly fee of $9. Many of Flexcar’s vehicles are Honda Motor Co.’s Civic hybrids, which can travel as far as 51 miles on a gallon of gas and produce less pollution by running on a gasoline-powered engine with an electric motor.