---
title: "Moving observer: bicycle racer on 800 m bikeway"
subject: "Transportation Engineering II"
chapter: 1
key: "semester_7/transportation_engineering_ii:moving-observer-bicycle-800m"
source: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/moving-observer-bicycle-800m
site: BCT Engineering
---

# Moving observer: bicycle racer on 800 m bikeway

Transportation Engineering II · Chapter 1: Traffic Engineering

- Asked in: 2076 Asoj, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/moving-observer-bicycle-800m
- Whole chapter: https://www.bctengineer.com/md/semester_7/transportation_engineering_ii/chapter-1

## Question

A bicycle racer practices everyday in the morning. Her route includes a ride along 800 m bikeway and back. Since she is traffic engineer, she has made it a habit to count the numbers of cars in lane A that she meets while riding southward, the number of cars in lane A that overtake her while riding northward and the number of cars in lane A that she overtakes while riding northward as shown in table below. Find average traffic flow and time of lane A.

| Average Travel speed (km/hr) | Nos. of Vehicle met | Nos. of Overtaken Vehicle | Nos. of Overtaking Vehicle |
|---|---|---|---|
| 32 | 117 | 10 | 74 |
| 34 | 93 | 25 | 41 |
| 32 | 30 | 15 | 5 |
| 33 | 70 | 18 | 9 |

## Short answer

Using moving observer method: average N_s=77.5, N_o=17, N_p=32.25 (y=-15.25), observer mean travel time 88.0 s. Flow q = (N_s + y)/(2t) = 1273 veh/h; lane mean travel time = 131.1 s (speed 22.0 km/h).

## Answer

The moving observer method gives the flow and mean travel time of lane A from counts made by the rider moving with and against the stream.

**Reading of the table:** the cars met while riding southward are the northbound stream of lane A ($N_s$). While riding northward, the cars overtaking her ($N_o$) and the cars she overtakes ($N_p$) are counted. Following the order of the question text, the column "overtaken" is read as cars that overtook her ($N_o$: 10, 25, 15, 18) and "overtaking" as cars she overtook ($N_p$: 74, 41, 5, 9).

#### Average values (4 runs)
Travel time on each run $t = 0.8/v$: 90.0, 84.7, 90.0, 87.3 s, giving a mean of $t_w = t_a = 88.0$ s $= 1.467$ min $= 0.02444$ h.

$$
\begin{aligned} \bar N_s &= \frac{117+93+30+70}{4} = 77.50\\ \bar N_o &= 17.00,\quad \bar N_p = 32.25,\quad y = \bar N_o - \bar N_p = -15.25 \end{aligned}
$$

#### Flow
$$
q = \frac{\bar N_s + y}{t_w + t_a} = \frac{77.50 + (-15.25)}{2(0.02444)} = 1273\ \text{veh/h}
$$

#### Mean travel time of lane A
$$
\bar t = t_w - \frac{y}{q} = 0.02444 - \frac{(-15.25)}{1273} = 0.03642\ \text{h} = 131.1\ \text{s}
$$

Mean speed $= 0.8/0.03642 = 22.0$ km/h.

**Answer: average flow of lane A = 1273 veh/h; average travel time = 131.1 s (2.19 min) over the 800 m, i.e. a stream speed of 22.0 km/h.**

Note: if the column headings are read literally the other way round ("overtaking" = cars that overtook her, $\bar N_o = 32.25$; "overtaken" = cars she overtook, $\bar N_p = 17.00$), then $y = +15.25$, $q = (77.50 + 15.25)/0.04889 = 1897$ veh/h and $\bar t = 0.02444 - 15.25/1897 = 0.01640$ h $= 59.1$ s (stream speed 48.8 km/h). State the reading you use in the exam.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which formula gives the flow in the moving observer method here?
   A. q = (Ns + y)/(tw + ta)
   B. q = Ns x (tw + ta)
   C. q = y/(tw + ta)
   D. q = Ns/y
   Answer: A. q = (Ns + y)/(tw + ta), where y = No - Np. (Key point: Flow formula)

2. How is the travel time of each run found?
   A. t = 0.8 x v
   B. t = v/0.8
   C. t = 0.8/v
   D. t = 800/60
   Answer: C. t = distance/speed = 0.8 km / v, e.g. 0.8/32 h = 90 s. (Key point: Travel time per run)

3. Using the answer's reading, what is y = No - Np?
   A. +15.25
   B. -15.25
   C. 77.5
   D. 32.25
   Answer: B. No = 17.00 and Np = 32.25 so y = -15.25. (Key point: Correction y)

4. What average flow of lane A results?
   A. About 623 veh/h
   B. About 1273 veh/h
   C. About 2546 veh/h
   D. About 77 veh/h
   Answer: B. q = (77.5 - 15.25)/(2 x 0.02444) = 1273 veh/h. (Key point: Result)

## Related in Transportation Engineering II

- [Moving observer: car counts on 800 m road](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Amoving-observer-car-800m-20kmph) — Transportation Engineering II, chapter 1

## Related in other subjects

- [Traffic numerical: 800 calls, 50 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-800-calls-50-lost) — Telecommunications, chapter 6, asked 6×
- [Resolution: Sita and her umbrella](https://www.bctengineer.com/question.md?key=semester_4%2Fdiscrete_structure%3Aresolution-sita-umbrella) — Discrete Structure, chapter 1
- [The Mother of a Traitor: "Is it she?"](https://www.bctengineer.com/question.md?key=semester_5%2Fcommunication_english%3Ais-it-she-mother-of-traitor) — Communication English, chapter 2