Elia rode her bicycle from her house to the beach at a constant speed of 18 kilometers per hour, and then rode from the beach to the park at a constant speed of 15 kilometers per hour. The total duration of the rides was 1 hour and the distances she rode in each direction are equal. Let b be the number of hours it took Elia to ride from her house to the beach, and p the number of hours it took her to ride from the beach to the park.