Hector can run 400 metres in 66 seconds - OCR - GCSE Maths - Question 22 - 2018 - Paper 1

To establish if Hector can run 5 kilometres in less than 14 minutes, we first need to convert both distances and times into a consistent format.

1. Distance Conversion: 5 kilometres can be expressed in metres:

   $5 \text{ km} = 5 \times 1000 \text{ m} = 5000 \text{ m}$

2. Determine Running Rate: If Hector can run 400 metres in 66 seconds, we can calculate his time for 5000 metres by determining how many sets of 400 metres fit into 5000 metres:

   $\frac{5000 \text{ m}}{400 \text{ m}} = 12.5$

   This means Hector would need to run the 400 metres 12.5 times to cover 5000 metres.

3. Calculate Total Time: Now, we multiply the time taken to run 400 metres by the number of laps:

   $12.5 \times 66 \text{ seconds} = 825 \text{ seconds}$

4. Convert Total Time to Minutes: To determine if this time is less than 14 minutes, we convert seconds to minutes:

   $\frac{825 \text{ seconds}}{60} = 13.75 \text{ minutes}$

Thus, Hector would take approximately 13.75 minutes, which is indeed less than 14 minutes.