Anya, Sophia, Masha, and Mike went to New York City to see a few Broadway shows. They stayed on
a floor in a small hotel which had four rooms along one long hallway. Anya was staying in the first
room, Sophia in the second room, Masha in the third room, and Mike in the fourth room, at the
opposite end of the hall from Anya. The elevator was along the hallway, exactly halfway between
Sophia's door and Masha's door. One afternoon, Sophia and Masha got out of the elevator and
walked 90 feet to Mike's door to say hello. Then they walked back the other direction all the way
down the hall to Anya's door to leave a note. The total distance from Mike's door to Anya's door
was 160 feet. Then they turned around and walked 30 feet to Sophia's door. How far did Masha
have to walk to return from Sophia's door to her own room's door?