Solution :
The distance between the starting point and the end point, = 10 light years
But due to the relativistic motion of Bob and Charlie, the distance will be reduced following the Lorentz contraction. The contracted length will be different since they are moving with different speeds.
For Bob,
Speed of Bob's rocket with respect to Alice,
So the distance appeared to Bob due to the length contraction,
Therefore, the time required to finish the race by Bob is
= 10.143 year
For Charlie,
Speed of Charlie's rocket with respect to Alice,
So the distance appeared to Charlie due to the length contraction,
The time required to finish the race by Charlie is
= 5.77 year