Plain scale for bus travel time

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.

 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.