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?