---
title: "Plain scale for bus travel time"
subject: "Surveying I"
chapter: 1
key: "semester_3/surveying_i:plain-scale-bus-time"
source: https://www.bctengineer.com/q/semester_3/surveying_i/plain-scale-bus-time
site: BCT Engineering
---

# Plain scale for bus travel time

Surveying I · Chapter 1: Introduction

- Asked in: 2081 Bhadra, 4 marks
- Video: [Plane scale problem-4 data given in the terms of speed /distance and time.](https://www.youtube.com/watch?v=NvCC27li1xU) — Vikash Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/plain-scale-bus-time
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-1

## Question

The distance between two stations is 210 km. A bus covers this distance in 7 hours. Construct a plain scale to measure time upto a single minute. RF is 1/200,000. Indicate the distance travelled by bus in 29 minutes on the scale. Scale can read maximum 30 km.

## Short answer

Speed is 30 km/h. Scale length 15 cm represents 30 km (60 min). Main divisions of 2.5 cm = 10 min, sub-divisions of 0.25 cm = 1 min. Distance in 29 min = 14.5 km (7.25 cm on scale).

## Answer

#### Given and basic values
- Distance = 210 km, time = 7 h, so speed $= 210/7 = 30$ km/h.
- RF $= 1/200{,}000$, so 1 km on the ground $= 100{,}000$ cm $/ 200{,}000 = 0.5$ cm on the scale.
- Maximum reading $=$ 30 km $=$ 1 hour $=$ 60 minutes.

#### Scale length
$$
\text{Length} = 30\ \text{km} \times 0.5\ \text{cm/km} = 15\ \text{cm}
$$

Distance per minute $= 30/60 = 0.5$ km, so 1 minute $= 0.5 \times 0.5 = 0.25$ cm.

#### Construction
1. Draw a line 15 cm long and divide it into 6 equal main divisions of 2.5 cm each. Each main division is 10 minutes (5 km).
2. Mark 0 at the end of the first division from the left, and number the others 10, 20, 30, 40, 50 min.
3. Divide the first (left) main division into 10 equal sub-divisions of 0.25 cm, each 1 minute (0.5 km).
4. Draw a parallel line below, and draw the scale as a rectangle (about 0.5 cm high). Write the distance in km on the same scale: 0, 5, 10, ... 25 km.

```text
 min 10   5    0    10   20   30   40   50
     |....|....|----|----|----|----|----|
 km  5    2.5  0     5    10   15   20   25
          <-----  RF 1/200,000  ----->
```

#### Distance covered in 29 minutes
29 min = 2 main divisions (20 min) + 9 sub-divisions (9 min).

$$
\text{Distance} = 29 \times 0.5 = 14.5\ \text{km}
$$

On the scale the length is $29 \times 0.25 = 7.25$ cm. Mark the point 2 main divisions to the right of 0 and 9 sub-divisions to the left of 0. Place the divider on these points.

**Answer: distance travelled in 29 minutes = 14.5 km (7.25 cm on the scale); scale length = 15 cm.**

## Check yourself

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

1. The bus speed is
   A. 7 km/h
   B. 30 km/h
   C. 210 km/h
   D. 60 km/h
   Answer: B. 210 km / 7 h = 30 km/h. (Key point: Speed)

2. With RF 1/200,000, the scale for 30 km is
   A. 15 cm long
   B. 30 cm long
   C. 7.5 cm long
   D. 1.5 cm long
   Answer: A. 1 km = 0.5 cm, so 30 km = 15 cm. (Key point: Scale length)

3. What does 1 minute represent on the scale?
   A. 1 km, or 0.5 cm
   B. 5 km, or 2.5 cm
   C. 0.5 km, or 0.25 cm
   D. 0.25 km, or 0.5 cm
   Answer: C. 30 km/h = 0.5 km per min = 0.25 cm. (Key point: Per minute)

4. The distance travelled in 29 minutes is
   A. 29 km
   B. 15 km
   C. 7.25 km
   D. 14.5 km
   Answer: D. 29 x 0.5 = 14.5 km (7.25 cm on the scale). (Key point: 29 minutes)

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