Question $2(15\%)$

A new development that will be in operation after $10$ years is expected to generate

$1400$ trips. All the trips are directed to town A $($population of $110,000$ persons and

$2\%$ annual growth rate$)$ and town B $($population of $135,000$ persons and $3\%$ annual

growth rate$).$ To reach town B from the new development, the users may use route $1$

$($with a total length of $17km$ and expected future traffic of $1400$ trips$)$ or route$2($with

a total length of $15km$ and expected future traffic of $1200$ trips$).$ The two routes have

the following volume$-$travel time equations:

$TT=3\mathrm{.}5+1\mathrm{.}3(\frac{V}{2000})$ Route $1$

$TT=4\mathrm{.}1+1\mathrm{.}4(\frac{V}{1750})$ Route $2$

Where: $TT=$ travel time per kilometer, and $V=$ total volume on the path

a$.$ If the trips are distributed according to the population, what is the number of

trips going to towns A and $B?(5\%)$

b$.$ What should be the flow on routes $1$ and $2$ in order to have the same travel

time on both routes? $(10\%)$