Hand written solution required

Q1) [8+8 - 16 Marks] Agnes is travelling in a train with a velocity of 0.6c relative to Betty who is sitting in her laboratory. Agnes fires a stream of X particles towards the front wall of her carriage (in the same direction she in travelling) and measures the velocity of the particles to be 0.8c. X particles are unstable and Betty measures their mean lifetime at rest to be T = 0.625 x 10 #s in her lab. a) What is the velocity of the X particles as measured in Betty's frame? b) Betty observes that -= 13.5% of the X particles hit the front wall of Agnes carriage before decaying. What is the distance to the front wall in Agnes' frame