A train travelled along a track in 110 minutes, correct to the nearest 5 minutes - Edexcel - GCSE Maths - Question 17 - 2017 - Paper 3

To determine whether the average speed of the train could have been greater than 160 km/h, we first need to calculate the speed based on the distance travelled and the time taken.

1. Calculate the Time Range: Since the time is given as 110 minutes, correct to the nearest 5 minutes, the time could actually range from:

   • Minimum: 110 - 2.5 = 107.5 minutes
   • Maximum: 110 + 2.5 = 112.5 minutes

2. Convert to Hours:

   • Minimum Time in Hours: $T_{min} = \frac{107.5}{60} \approx 1.7917 \text{ hours}$
   • Maximum Time in Hours: $T_{max} = \frac{112.5}{60} \approx 1.875 \text{ hours}$

3. Calculate the Possible Distances: Assuming the track is 270 km long, the speed can be calculated using: $Speed = \frac{Distance}{Time}$

   • Minimum Speed: $S_{min} = \frac{270 \text{ km}}{1.875 \text{ hours}} \approx 144 \text{ km/h}$
   • Maximum Speed: $S_{max} = \frac{270 \text{ km}}{1.7917 \text{ hours}} \approx 150.6 \text{ km/h}$

4. Conclusion: As both calculated speeds (144 km/h and approximately 150.6 km/h) are below 160 km/h, we can conclude that the average speed of the train could not have been greater than 160 km/h.