Need Help getting the part b. I\'m not sure if I\'m using awrong equation or if

Question

Need Help getting the part b. I'm not sure if I'm using awrong equation or if my algebra is messing me up. I'd appreciateany help I can get - Lifesaver.
The International Space Federation constructs a new spaceshipthat can travel at a speed of 0.900c. Mary, the astronaut, boards thespaceship to travel to Barnard's star, which is the second neareststar to our solar system after Alpha Centauri and is 5.98 ly away.After reaching Barnard's star, the spaceship travels slowly aroundthe star system for 3 years doing researchbefore returning back to Earth. (a) How much time does the journey take?(years)
(b) How much older is her twin Frank when she returns?(years) Need Help getting the part b. I'm not sure if I'm using awrong equation or if my algebra is messing me up. I'd appreciateany help I can get - Lifesaver.
The International Space Federation constructs a new spaceshipthat can travel at a speed of 0.900c. Mary, the astronaut, boards thespaceship to travel to Barnard's star, which is the second neareststar to our solar system after Alpha Centauri and is 5.98 ly away.After reaching Barnard's star, the spaceship travels slowly aroundthe star system for 3 years doing researchbefore returning back to Earth. (a) How much time does the journey take?(years)
(b) How much older is her twin Frank when she returns?(years)

Explanation / Answer

The time taken for the whole journey, according to Frank is 5,98 ly/0,9 c *2+3=16,3 (y) While according to Mary, the time taken for going to Barnard and goback is T0=5,98ly/0,9 c *2 /=13,28 * sqrt(1-0,9^2)=5,78 y the total time is 5,78+3=8,78(y) So Frank is 7,5 years older than Mary

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