MDOT is supposed to decide on adding a passing lane in an upgrade segment of a

$2-$lane highway in a rural area with the following features:

$-$ Segment is located on an $4\%$ upgrade with a length of $1,500$ ft

$-$ Speed limit $=50$ mph for all the vehicles

$-$ AADT $=4,500$

$-$ Truck volume $=10\%$ of AADT

$-$ Peak flow direction belongs to downgrade lane

$-$ Lane Width $=11$ ft

$$ Should MDOT add a passing lane here? Why?

$$ Assuming that we need a passing lane here, how much should be the length

of passing lane and its taper?