Answer:
correct answer is c. 49.4 min
Explanation:
given data
course time = 60 minutes
arrive rate A(t) = 1.8 + 0.25t - 0.0030t²
departure rate function D(t) = 1.4 + 0.11t
to find out
maximum queue length occur
solution
first we get here total vehicle arrive after time = t is
total vehicle =
total vehicle = 1.8t + .............1
and
now we get here here total vehicle departed after time = t is
total vehicle departed =
total vehicle departed = 1.4 t + ..............2
so length at timer t is equation 1 - equation 2
so length at timer t = 1.8t + - 1.4 t +
and here for maximum length = 0
so put here equation = 0 we get t
1.8t + - 1.4 t + = 0
solve it we get
t = 49.40 min
so correct answer is c. 49.4 min