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AQA GCSE · Question 04 · Ratio Proportion and Rates of Change
A map has a scale of 1 : 4000
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On the map, the distance from a station to a museum is 7 cm.
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Is the actual distance from the station to the museum more than 300 m?
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Show working to support your answer.
A map has a scale of 1 : 4000
<br>
On the map, the distance from a station to a museum is 7 cm.
<br>
Is the actual distance from the station to the museum more than 300 m?
<br>
Show working to support your answer.
How to approach this question
1. Use the scale to find the actual distance in the same units as the map distance (cm). Multiply the map distance by the scale factor.
2. Convert the actual distance from centimetres to metres. Remember that 1 m = 100 cm.
3. Compare your calculated distance in metres with 300 m.
4. State your conclusion clearly (Yes or No) based on the comparison.
Full Answer
**Step 1: Calculate the actual distance in cm.**
The scale is 1 : 4000, which means 1 cm on the map represents 4000 cm in reality.
The map distance is 7 cm.
Actual distance = 7 cm × 4000 = 28000 cm.
**Step 2: Convert the actual distance to metres.**
There are 100 cm in 1 metre.
Actual distance in metres = 28000 cm / 100 = 280 m.
**Step 3: Compare the actual distance with 300 m.**
The actual distance is 280 m.
280 m is less than 300 m.
**Conclusion:**
No, the actual distance is not more than 300 m.
**Answer: No, with working shown.**
The map scale 1 : 4000 means that every 1 unit of distance on the map corresponds to 4000 units of distance in reality.
The distance on the map is 7 cm.
So, the actual distance is 7 cm * 4000 = 28000 cm.
The question asks to compare this to 300 m, so we need to convert our answer to metres.
Since 100 cm = 1 m, we divide by 100:
28000 cm / 100 = 280 m.
Now we compare: Is 280 m more than 300 m? No, it is not.
Therefore, the answer is No.
Common mistakes
✗ Incorrectly converting between cm and m (e.g., dividing by 10 or 1000).
✗ Dividing by the scale factor instead of multiplying.
✗ Comparing 28000 cm directly with 300 m without converting units, leading to an incorrect conclusion.
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