Time Dilation: Finding Velocity & Age Difference

[Nitric]

1. Twins Abby and Billy separate. Abby travels at a uniform speed (except for the brief turn-around period) to a star 4.2 light years away and, upon returning, finds that she is 5.2 years younger than Bill. How fast was Abby traveling? By how much has Bill aged during the period Abby was traveling?



2. T'=2L/C
T' = T_o=sqrt(1-v^2/c^2)
deltaT = T' - T_o



3. So far I have found the time dilation using T'=2L/C => 2(4.2)/C = 2.8^-8
I tried using T' = T_o=sqrt(1-v^2/c^2) to find velocity, is that correct? I'm not sure what T_o is.

 

[Carid]

TimeExperiencedByBill = TimeExperiencedByAbby + 5.2years

TimeExperiencedByAbby = TimeExperiencedByBill * SQRT(1-V²/C²)

V = DistanceTravelled/TimeExperiencedByBill

 

[Nitric]

I figured out the velocity, which is 0.9c. How do I find how much Bill aged during the time Abby was traveling?

 

[Carid]

I think that if you manipulate the three equations I provided you should be able to come up with the value of TimeExperiencedByBill

 

[Nitric]

lol i figured it out by using v=d/t