Please reason step by step, and put your final answer within \boxed{}.
During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. She stopped again after she traveled a certain fraction of the distance remaining between her first stop and her destination, and then she drove the remaining 150 miles to her destination. The total distance from Maria's starting point to her destination was 400 miles. What fraction of the remaining distance did Maria travel between her first and second stops?
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