1. **State the problem:** A train travels a track measured as 270 km (nearest 10 km assumed initially) in 110 minutes (nearest 5 minutes). We want to check if the average speed could be greater than 160 km/h. 2. **Convert time to hours:** Since 110 minutes is measured to the nearest 5 minutes, the actual time $t$ lies in the interval: $$105 \leq t \leq 115 \text{ minutes}$$ Convert to hours: $$\frac{105}{60} \leq t \leq \frac{115}{60}$$ $$1.75 \leq t \leq 1.9167 \text{ hours}$$ 3. **Determine distance bounds:** Jake assumes the track length is 270 km measured to the nearest 10 km, so the actual distance $d$ lies in: $$265 \leq d \leq 275 \text{ km}$$ 4. **Calculate maximum possible average speed:** Average speed $v = \frac{d}{t}$. To check if $v > 160$ km/h is possible, use the maximum distance and minimum time: $$v_{max} = \frac{275}{1.75} = 157.14 \text{ km/h}$$ 5. **Interpretation:** Since $157.14 < 160$, the average speed could not have been greater than 160 km/h under these assumptions. 6. **Part (b) explanation:** If the track was actually measured to the nearest 5 km, the distance bounds become: $$267.5 \leq d \leq 272.5 \text{ km}$$ This reduces the uncertainty in distance, making the maximum possible speed closer to: $$\frac{272.5}{1.75} = 155.71 \text{ km/h}$$ This smaller range confirms the average speed is even less likely to exceed 160 km/h. **Final answer:** No, the average speed could not have been greater than 160 km/h.