# How to calculate ground speed using a map with a known scale and time?

If an aircraft flies from point A to B for a distance of 8cm on a chart of 1:1,000,000 in 18 minutes, What’s the ground speed?

It’s a multiple choice question and the possible answers are in ratios.
(#45 in the image)

A. $$1:1,105,550$$
B. $$1:1,250,000$$
C. $$1:1,740,740$$
D. $$1:1,074,740$$

I can’t change the question but I can explain how it is related to aviation. The question is from flight dispatcher module Air Navigation, where by in dispatching the aircraft we must know about places where aerodromes are located passing etc and so we learn about maps and charts.. am not off topic the question is 100% aviation related

• It's possible that the test creator made a mistake--it happens! It could be that they accidentally mixed up the answers to two questions while editing the test. I think you should ask your instructor or aide about the possibility that there's a mistake. – Wayne Conrad Aug 27 '19 at 19:32
• Angie, I appreciate what you are doing, trying to figure out which answer is correct. I firmly believe that none of the answers can be. The reason is that the correct answer is a speed, which will be expressed in distance-per-time: kilometers-per-hour, miles-per-hour, nautical-miles-per-hour (or Knots for short). But the answers you are supposed to chose from are dimensionless ratios. Speed isn't expressed as a ratio. It just isn't. That's why I and others are certain that there is a mistake on the test. – Wayne Conrad Aug 27 '19 at 19:51
• Please let us know what the answer/explanation is. I'm very curious to know. – abelenky Aug 27 '19 at 20:14
• What I really want to know is did you and/or any of your classmates figure out that the test was broken before asking the internet? – quiet flyer Aug 28 '19 at 13:22
• I'm tend to disagree with your last edit. you can replace "flown by an aircraft" by "traveled by a train" in the question without changing it. Yet, your question was not closed because it was off topic but because it was unclear, and your last edit clarifies it. – Manu H Sep 2 '19 at 5:20

## 1 Answer

If a plane traveled $$8\ \mathsf{cm}$$ on a map with a scale of $$1:1\ \mathsf{million}$$, then it traveled $$8\ \mathsf{million\ cm}$$ in the real-world.

$$8\ \mathsf{million\ cm} = 80,000\ \mathsf{meters} = 80\ \mathsf{km}$$

Convert 80 km in 18 minutes to a speed of kilometers per hour:

$$\frac{80\ \mathsf{km}}{18\ \mathsf{min}} \cdot \frac{60\ \mathsf{min}}{1\ \mathsf{hour}} = 266.6 \frac{\mathsf{km}}{\mathsf{hr}}$$

Groundspeed is traditionally expressed in knots:

$$266.6\ \mathsf{kph} \cdot \frac{0.54\ \mathsf{kts}}{1\ \mathsf{kph}} = 144\ \mathsf{kts}$$

To put this in perspective, 144 kts is a bit fast for a Cessna 172, unless it has a good tailwind, but not at all unreasonable for many small high-performance planes.

The answers to question #44 don't make sense. The question is "The scale of the chart is...", but the possible answers are all KTS (knots).

The answers to #44 and #45 are clearly reversed.
However, the right answer of 144 kts, is not listed in the possible answers.

In general, I think that test is extremely poor quality.

Question #43 (movement of the earth around the sun) may not even be related to aviation.

• Thank you, can you help me to convert the answer to ratio as per scale please – Angie Aug 27 '19 at 19:17
• @Angie No, that doesn't make sense. The answer is 144 knots. None of the answer choices you listed make sense as an answer to this question. – Terran Swett Aug 27 '19 at 19:24
• for #43, Revolution is a perfectly fine answer. – Federico Aug 28 '19 at 12:02