Question

While traveling along and against the traffic stream, a moving observer measured the relative flows as 50 vehicles/hr and 200 vehicles/hr, respectively. The average speeds of the moving observer while travelling along and against the stream are 20 km/hr and 30 km/hr, respectively. The density of the traffic stream (expressed in vehicles/km) is

• A. 3

Answer 1

The correct option is A 3
Relative flow along the stream=$q-K{V}_{\omega }$
Relative flow against the stream =$q+K{V}_a$
when, q= traffic flow
k = traffic density
$V_{\omega }$ =velocity of test vehicle along the stream
$V_a$=velocity of test vehicle against the stream
$\Rightarrow q-K{V}_{\omega }=50\Rightarrow q-K\times 20=\mathrm{50...}\left(A\right)$
$q+K{V}_a=200\Rightarrow q+K\times 30=200...\left(B\right)$
From eqn. (A) and (B), we have
$-50K=-150$
$\Rightarrow K=3Veh/km$