First Homework Assignment

1. The problem statement, all variables and given/known data

1. Two firecrackers explode at the same place in the laboratory and are separated by a time of 3 years as measured on a lab clock.

(a) What is the spatial distance between these two events in a rocket in which the events are separated in time by 5 years as measured on rocket clocks?

(b) What is the relative speed of the rocket and the lab frames?

2. Relevant equations

? – I am not exactly sure, but, I believe one relevant equation is:
t` = γ (τ – βx)
x` = γ (x – βτ)

3. The attempt at a solution

Trying to find x:

t`/γ = τ – βx

βx = -t`/γ + τ

x = -t`/γ + τ

Thank you so much for any help. This is my first Physics course so if you don’t mind could you assume I know literally nothing, like less than an ant?
My problem is I am thinking: what is the velocity? I am really lost/confused

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