Problem $2(5+15=20)$

The market demand function of transportation service is $D(GP)=100-20\sqrt[\phantom{2}]{GP}$ where $GP$

denote the generalized price which is defined as $GP=p+0\mathrm{.}5t$ where $p$ is travel cost in

dollar and $t$ is travel time in minute. Suppose a transportation investment project reduces

the travel time from $20$ minutes into $16$ minutes while the travel cost is fixed to be$10$ dollars.

$(1)$ How much is the value of time?

$(2)$ Calculate the user's benefit stemming from the project.

Notes: you may use $\sqrt[\phantom{2}]{2}=1\mathrm{.}4$ and $\sqrt[\phantom{2}]{5}=2\mathrm{.}2.$