I like this problem, I got the same answer. the way I did it
Given, Q = 63.4k - 0.46k^2
At maximum flow, dQ/dk = 0
or, 63.4 - 0.46 * 2k = 0
or k= 68.91 veh/mi (critical/optimum density)
Q = 63.4 * 68.91 - 0.46 * (68.91) ^2 = 2184.54 veh/hr (maximum flow)
Critical speed = maximum flow /...