Twins, A and B. A goes off in a straight line traveling at .96c for 7 years as measured on his clock, then reverses and returns at half the speed. B remains at home. When they return, what is the difference in ages between A and B?
The Attempt at a Solution
My answer is 19.958 yrs. I got this by calculating time dilation for B in the 7 year leg of the trip of A, giving me 25 years. Then I calculated the distance A traveled in 7 years by multiplying .96c times time. I'm a bit iffy on that step but let me continue.
Having found that distance I again found the time by doing the simple distance over velocity and I get 14 years for A, then doing time dilation for B, I get 15.95 years, so A ages 21 years and B ages 40.95 years, thus their age difference is 19.95 yrs.
My question is, is this right? Do I not have to take into account length contraction to calculate the distance A traveled in 7 years or is it because I'm using a relative velocity that makes this calculation ok?