Question $3(10\%)$

An estimation procedure for a mode choice model of the nested Logit structure, found

that $U_T-a_T+$ Logsum with $a_T-1\mathrm{.}04$ and $=0\mathrm{.}91.$ The utility expression in the

considered city is:

$U_k=a_k-0\mathrm{.}010x_1-0\mathrm{.}015x_2-0\mathrm{.}021x_3-0\mathrm{.}004x_4$

Where,

$x_1=$ Travel time $(min.)x_2=$ Access and egress time $(min)$

$x_3=$ Waiting time $(min)x_4=$ Out $of$ pocket cost $(cents)$

The characteristics of the modes $($Auto$,$ Bus, and Rail$)$ are shown in Table $3.$

Table $3$: Modes' characteristics.

Determine the bus travel time so that the transit will attract $43\%$ of the users.