Question: Convert $200$ km/h to m/s. Hence write down $60$ km/h in m/s to 3 significant figures.

Step 1. Write the speed as a fraction and convert top and bottom separately:

$$200 \text{ km/h} = \dfrac{200 \text{ km}}{1 \text{ h}} = \dfrac{200 \times 1000 \text{ m}}{3600 \text{ s}}$$

Step 2. Simplify:

$$= \dfrac{200\,000}{3600} = \dfrac{500}{9} \text{ m/s} \approx 55.6 \text{ m/s}$$

Step 3. Spot the reusable factor: km/h → m/s is always $\times \dfrac{1000}{3600} = \div 3.6$.

Step 4. Apply it:

$$60 \text{ km/h} = 60 \div 3.6 = 16.7 \text{ m/s} \quad (3 \text{ s.f.})$$

Check. m/s numbers should come out smaller than the km/h they came from (a metre-per-second is faster than a kilometre-per-hour... in fact $1$ m/s $= 3.6$ km/h, so the m/s figure is the smaller one). $55.6 < 200$ ✓.

⚠ Watch out: Going the other way (m/s → km/h) is $\times 3.6$: $10$ m/s $= 36$ km/h. Pick the direction by sense-checking the size of the answer — if converting to m/s made the number bigger, the factor went the wrong way.

Question: A man cycled for $2$ hours at an average speed of $18$ km/h, then walked for another $2$ hours at an average speed of $5$ km/h. Find the total distance travelled and his average speed for the whole journey.

Step 1. Distance of each stage ($\text{distance} = \text{speed} \times \text{time}$):

$$\text{Cycling: } 18 \times 2 = 36 \text{ km}, \qquad \text{Walking: } 5 \times 2 = 10 \text{ km}$$

Step 2. Total distance:

$$36 + 10 = 46 \text{ km}$$

Step 3. Average speed is defined only one way:

$$\text{Average speed} = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{46}{4} = 11.5 \text{ km/h}$$

Step 4. Compare with the tempting wrong answer: $\dfrac{18+5}{2} = 11.5$… which happens to match here only because the two times were equal. The definition, not the coincidence, is what earns marks — and the next card shows a journey where averaging the speeds fails.

⚠ Watch out: Never average the speeds. Always rebuild total distance and total time separately, then divide. If a stage gives time in minutes, convert to hours before dividing — mixed units are the other classic average-speed killer.

Question: Joy travelled $\dfrac{2}{3}$ of her journey at $80$ km/h and the remaining journey at $60$ km/h. The total distance was $180$ km. How long did she take for the entire journey?

Step 1. Turn the fraction into distances:

$$\text{First part} = \dfrac{2}{3} \times 180 = 120 \text{ km}, \qquad \text{Second part} = 180 - 120 = 60 \text{ km}$$

Step 2. Time for each part ($\text{time} = \text{distance} \div \text{speed}$):

$$t_1 = \dfrac{120}{80} = 1.5 \text{ h}$$

Step 3.

$$t_2 = \dfrac{60}{60} = 1 \text{ h}$$

Step 4. Add the times:

$$\text{Total time} = 1.5 + 1 = 2.5 \text{ hours}$$

(And if the question went on to ask for her average speed: $\dfrac{180}{2.5} = 72$ km/h — note it is not the simple average of $80$ and $60$, because she spent longer at the slower speed.)

⚠ Watch out: The fraction $\frac{2}{3}$ applies to distance, not time — resist writing $\frac{2}{3}$ of the time at $80$ km/h. Convert to actual kilometres first, and keep each stage's $D$–$S$–$T$ triangle separate until the final addition.