Service is to be provided along a circular bus route of length D $=20$ km that visits n $=24$ stops.

Buses travel at speed v $=20$ km$/$hr and waste a fixed amount of time

$\backslash$tau $=1$ min at each stop $($for

all activities, including passenger boarding and alighting, door opening and closing, etc.$).$

Demand is steady with the same rate $($q $=0\mathrm{.}25$ pax$/$hr$)$ between every origin$-$destination pair. The

contract with the transit agency stipulates that the agency must serve this route with an average

service time across all passengers equal to T $=0\mathrm{.}80$ hrs$.$ This time is the sum of the average

waiting time at an origin and the average riding time. How many buses $($at the minimum$)$ would it need to run both clockwise and counter$-$

clockwise routes?