162.3853

Based on previous discussion, the solution should have the following feature: (1)person 1 always drive (2) they all arive at the terminal at the same time.

Assume the total time it takes for them to finish is t,
and assume for each person i, the total time that he rides the car is t_i, for i = 2,3,4,5
we have
2(t-t_2)+10t_2 = 1000
3(t-t_3)+10t_3 = 1000
4(t-t_4)+10t_4 = 1000
5(t-t_5)+10t_5 = 1000
10[(t_2+t_3+t_4+t_5)/2-(t-(t_2+t_3+t_4+t_5)/2))] = 1000

Solve for t to get t = 162.3853

Anything wrong with this method?