Answer:
14.625 years
Explanation:
Because acceleration/deceleration are negligent we can simplify this problem into 2 basic parts:
First: how long before the astronaut arrives? Since the speed of the craft is 0.8 times the speed of light and the distance to travel is 6.5 light-years, the equation to answer this part is:
0.8t=6.5
solve for t by dividing by 0.8
t=6.5/0.8 or 8.125
so, she will arrive in 8.125 years.
Then, once she sends her message, it will travel towards earth at 1 times the speed of light or:
1.0t=6.5 which is just t=6.5
so, her message will arrive back to Earth (8.125+6.5) 14.625 years after takeoff.