Question

A student riding a bicycle on a 5 km one-way street takes 40 minutes to reach home. The student stopped for 15 minutes during this ride. 60 vehicles overtook the student (assume the number of vehicles overtaken by the student is zero) during the ride and 45 vehicles while the student stopped. The speed of vehicle stream on that road (in km/hr) is

1. 7.5
2. 12
3. 40
4. 60

Answer 1

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