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Dean drives a distance of 760 km in 9 hours - OCR - GCSE Maths - Question 14 - 2019 - Paper 1

Question 14

Dean drives a distance of 760 km in 9 hours. Robert drives a distance of 559 km in 6 hours 30 minutes. Who has the highest average speed? Show how you decide.

Worked Solution & Example Answer:Dean drives a distance of 760 km in 9 hours - OCR - GCSE Maths - Question 14 - 2019 - Paper 1

Step 1

Calculate Dean's Average Speed

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Answer

To find Dean's average speed, use the formula:

v = \frac{d}{t}

where:

$d$ is the distance (760 km)
$t$ is the time (9 hours)

Substituting the values, we get:

v_D = \frac{760 \text{ km}}{9 \text{ h}} \approx 84.44 \text{ km/h}

Step 2

Calculate Robert's Average Speed

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Answer

Next, we calculate Robert's average speed using the same formula:

v = \frac{d}{t}

His distance is 559 km and his time is 6 hours and 30 minutes, which is equivalent to 6.5 hours. Thus:

v_R = \frac{559 \text{ km}}{6.5 \text{ h}} \approx 86.06 \text{ km/h}

Step 3

Compare the Average Speeds

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Answer

Finally, we compare the two average speeds:

Dean's average speed is approximately 84.44 km/h.
Robert's average speed is approximately 86.06 km/h.

Since 86.06 km/h > 84.44 km/h, Robert has the highest average speed.

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