Question

A tourist visiting a city holds a map prepared at a scale of 1:25000. The tourist measures the distance between place A and place B in the city as 12.0 cm on the map. Assuming both the places are connected by a straight road, the distance (in km) the tourist needs to walk from A to B is __________ (rounded off to the nearest integer).

Hint:

Multiply the map distance by the scale factor 25000, then convert cm to km.

Answer 1

Correct Answer: 3

Instead of converting to centimetres first, work out how many real kilometres correspond to one centimetre on this particular map, then scale up by the measured length.

1. Find the ground length of 1 cm on the map: the representative fraction 1:25000 means 1 cm on the map equals 25000 cm on the ground. Converting 25000 cm to metres: $25000/100 = 250$ m. Converting to km: $250/1000 = 0.25$ km. So every 1 cm on this map equals 0.25 km on the ground.
2. Scale up to the measured 12.0 cm: since the road is straight, the ground distance is simply the map distance times this per-cm ground length: $12.0 \times 0.25 = 3.0$ km.

Let's summarize:

• At scale 1:25000, 1 cm on the map = 0.25 km on the ground.
• 12.0 cm on the map then scales to $12.0 \times 0.25 = 3$ km.

So the tourist needs to walk $3$ km from A to B.