A freeway has a flow-density relationship approximated by

q=80k for 0  ≤ k ≤ 30

q=3200-26.67k for 30 ≤k ≤ 120

where k is in veh/km Flow on a particular day is approximately 2000veh/hr. At 10:00am an incident occurs which reduces capacity to 1600 veh/hr. The incident is cleared 45 minutes later and the flow returns to normal capacity of 2400 veh/hr. Assuming a smooth road with no ramps upstream, what are the speeds of the forming and clearing shockwaves of the queue upstream of the incident?.

a) What are the speeds of the forming and clearing shock waves that result?

b) When and where these shockwaves intersect?