A race is measured to have a distance of 10.6 km, correct to the nearest 0.1 km - Edexcel - GCSE Maths - Question 23 - 2022 - Paper 2

Sam's time for the race is 31 minutes and 48 seconds. To convert this to hours:

• Convert minutes to hours: 31 ext{ minutes} = rac{31}{60} ext{ hours}

• Convert seconds to hours: 48 ext{ seconds} = rac{48}{3600} ext{ hours}

Thus, total time in hours is:

t = rac{31}{60} + rac{48}{3600} ext{ hours}

Calculating gives:

$t ext{ (in hours)} ext{ } = 0.5300 ext{ hours}$

Now, we calculate average speed using the formula:

$v = \frac{d}{t}$

• For the lower bound of the distance:

$v_{lower} = \frac{10.55 ext{ km}}{0.5300 ext{ hours}} \approx 19.94 ext{ km/hour}$

• For the upper bound of the distance:

$v_{upper} = \frac{10.65 ext{ km}}{0.5300 ext{ hours}} \approx 20.06 ext{ km/hour}$

The calculated average speed bounds are approximately 19.94 km/hour to 20.06 km/hour, which suggests that the value of $v$ can be expressed with a precision of two decimal places, thus:

$v ext{ is } 20.0 ext{ km/hour}$

This degree of accuracy is appropriate as it reflects the accuracy of the original measurements.