Arron ran a distance of 5km at an average speed of 2.2m/s. How long did Arron run for? Give your answer in minutes and seconds, to the nearest second. (b) Claudine cycled a distance of 53 km in 2.7 hours. The distance is measured correct to the nearest km. The time is given correct to 1 decimal place. Calculate the lower and upper bounds of her average speed. Give your answers correct to 2 decimal places.

GCSE OCR Maths Angle Facts: Arron ran a distance of 5km at a

Arron ran a distance of 5km at an average speed of 2.2m/s - OCR - GCSE Maths - Question 15 - 2019 - Paper 1

Question 15

Arron ran a distance of 5km at an average speed of 2.2m/s. How long did Arron run for? Give your answer in minutes and seconds, to the nearest second. (b) Claudine... show full transcript

Worked Solution & Example Answer:Arron ran a distance of 5km at an average speed of 2.2m/s - OCR - GCSE Maths - Question 15 - 2019 - Paper 1

Step 1

How long did Arron run for?

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Answer

To determine how long Arron ran, we start with the formula for time:

t = \frac{d}{s}

In this case, the distance ( $d$ ) is 5 km and the speed ( $s$ ) is 2.2 m/s. First, we need to convert the distance into meters:

5 ext{ km} = 5000 ext{ m}

Now, substituting the values into the time formula:

t = \frac{5000 ext{ m}}{2.2 ext{ m/s}} \approx 2272.73 ext{ seconds}

Next, we convert seconds into minutes:

2272.73 ext{ seconds} \approx 37 ext{ minutes} \text{ and } 52.73 ext{ seconds}.

Rounding to the nearest second, Arron ran for approximately 37 minutes and 53 seconds.

Step 2

Calculate the lower and upper bounds of her average speed.

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Answer

The distance Claudine cycled is 53 km, with a measurement correct to the nearest kilometer. This implies:

Lower bound for distance = 52.5 km
Upper bound for distance = 53.5 km

The time taken is 2.7 hours, measured to 1 decimal place:

Lower bound for time = 2.65 hours
Upper bound for time = 2.75 hours

To find the average speed bounds, we apply the formula for average speed:

\text{Average Speed} = \frac{\text{Distance}}{\text{Time}}

Calculating the lower bound:

\text{Lower Bound Speed} = \frac{52.5 ext{ km}}{2.75 ext{ hours}} \approx 19.09 ext{ km/h}

Calculating the upper bound:

\text{Upper Bound Speed} = \frac{53.5 ext{ km}}{2.65 ext{ hours}} \approx 20.15 ext{ km/h}

Thus, Claudine's average speed is approximately:

Lower bound = 19.09 km/h
Upper bound = 20.15 km/h.

Arron ran a distance of 5km at an average speed of 2.2m/s - OCR - GCSE Maths - Question 15 - 2019 - Paper 1

Worked Solution & Example Answer:Arron ran a distance of 5km at an average speed of 2.2m/s - OCR - GCSE Maths - Question 15 - 2019 - Paper 1

How long did Arron run for?

Calculate the lower and upper bounds of her average speed.

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