TimeRiders (Book 1), by Alex Scarrow
Let me jump in and explain a few things before I really get started because the book is quite confusing at the start.
Liam was a steward on the sinking Titanic in 1912 and was about to drown; Maddy was on a plane with a ticking bomb in 2010 and was destined to die; Sal was about to get crushed to death in a fire in 2026. However, all three of them were rescued by an old man just before they died.
To cut a long story short, they wake up and find the old man who saved them. The man introduces himself as Foster and tells them he works for an agency called TimeRiders, the same agency that the three of them were recruited for. They would work with the agency and their goal would be to prevent time travellers from altering the past. When they went for a walk Maddy notices that they are in New York. However, the Twin Towers were still part of the skyline. Foster explained that they were in 2001 on 10th September, the day before the 9/11 attack. The three of them would be the New York group of the agency. The room where they woke up would be their field office where they would be living and working. The field office was in a time bubble of 48 hours and would reset on the night of 11th September. Therefore, the three of them would be reliving the 10th and 11th of September over and over.Each one of them had a particular role. Sal would be the observer as she was very observant and would immediately notice if anything had changed or if time travellers had changed anything. Maddy would be the analyst and would discover where and when the change occurred. Liam would be the field agent and would be sent back in time to fix and correct the timeline.