Two steamrollers begin \(100 \mathrm{~m}\) apart and head toward each other, each at a constant speed of \(1.00 \mathrm{~m} / \mathrm{s}\). At the same instant, a fly that travels at a constant speed of \(2.20 \mathrm{~m} / \mathrm{s}\) starts from the front roller of the southbound steamroller and flies to the front roller of the northbound one, then turns around and flies to the front roller of the southbound once again, and continues in this way until it is crushed between the steamrollers in a collision. What distance does the fly travel?