I asked this question earlier, but I am having trouble figuring out how the tutor got to the final equation.

My question: “I need help figuring up how to set up the problem to solve this. I can get the answer by playing with the numbers in excel so both ages are the same, but my instructor requires me to show how I calculated to actually get those numbers and just manipulating them does not count. The formula we are given to calculate this is:

T(rocket)=T(Earth)*SQRT(1-((v/c)^2)

The duration of the trip by YOUR clock is A + T = B + T*sqrt(1-v^2/c^2).

Explanation:

Suppose your age today is A, and your older relative’s age today is B.

You send him to travel at speed v for duration T by YOUR clock, so by his clock he will age by T*sqrt(1-v^2/c^2).

You want him and yourself to be of the same age when he returns, so you want A + T = B + T*sqrt(1-v^2/c^2).

From this equation you can find the duration of the trip needed (by YOUR clock) T = (B – A)/[ 1 – sqrt(1-v^2/c^2)] .”

Revised question: I was able to use the final equation and it works, but I am having trouble deriving how to get from A + T = B + T*sqrt(1-v^2/c^2) to T = (B – A)/[ 1 – sqrt(1-v^2/c^2). I have been playing with it algebraically and I can’t get it to make sense.