Correct Answer - Option 4 : 60

__Concept:__

**Moving observer method:**

Moving car or moving observer method of traffic stream measurement has been developed to provide simultaneous measurement of traffic stream variables. It has the advantage of obtaining the complete state with just three observers and a vehicle.

The mean speed by moving the observer method is given as follows

\({{\rm{V}}_{\rm{s}}} = \frac{{\rm{L}}}{{{{\rm{t}}_{\rm{w}}} - \frac{{{{\rm{m}}_{\rm{w}}}}}{{\rm{q}}}}}\)

t_{w} = Observation time when the observer is moving with the stream

m_{w} = Net vehicles overtake the observer when it is moving with the stream

q = Flow density when the observer is at rest in vehicles/min

__Calculation:__

Total time taken by the student to reach home = 40 min

Student’s stop time = 15 min

∴ t_{w} = 40 – 15 = 25 min = 0.416 hr

L = 5 km

\({\rm{q}} = \frac{{45{\rm{\;vehicles}}}}{{15{\rm{\;min}}}} = 3\frac{{{\rm{veh}}}}{{{\rm{minute}}}} = 180{\rm{\;veh}}/{\rm{hr}}\)

m_{w} = 60 vehicles

\({{\rm{V}}_{\rm{s}}} = \frac{{\rm{L}}}{{{{\rm{t}}_{\rm{w}}} - \frac{{{{\rm{m}}_{\rm{w}}}}}{{\rm{q}}}}}\)

\({{\rm{V}}_{\rm{s}}} = \frac{5}{{0.416 - \frac{{60}}{{180}}}} = 60.48{\rm{\;km}}/{\rm{hr}}\)

**Hence the speed of vehicle stream = 60 km/hr**