About 200 Muslim women have asked the Fitness USA workout chain to honor what they say was its promise to provide separate exercise times for women and men. They say they need single-sex workout times to accommodate Islam's standards of modesty. Arrwa Mogalli, 28, of Dearborn, Michigan, said that she agreed to buy a $1,465 lifetime membership with the chain after being promised that its Lincoln Park facility would be open only to women on certain days. This month, the gym in this southern Detroit suburb decided to open up a new part of the center to both sexes every day. Mogalli is among about 200 women with Fitness USA memberships who have signed a petition asking the chain to restore single-sex exercise days for the entire gym or to put up a divider so men and women cannot see each other while exercising. The company is reviewing the women's concerns, said Jodi Berry, administrative director for Fitness USA. But the company said that the women's written contracts say nothing about gender.