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Lara is a skier - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 3
Question 6
Lara is a skier. She completed a ski race in 1 minute 54 seconds. The race was 475 m in length. Lara assumes that her average speed is the same for each race. (a)... show full transcript
Worked Solution & Example Answer:Lara is a skier - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 3
Step 1
Using this assumption, work out how long Lara should take to complete a 700 m race.
Answer
To find out how long Lara should take to complete a 700 m race, we first need to calculate her average speed during the initial 475 m race.
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Convert the time taken into seconds: 1 minute 54 seconds = 1 × 60 + 54 = 114 seconds.
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Calculate the average speed: Speed = Distance / Time = ( \frac{475 \text{ m}}{114 \text{ s}} \approx 4.1737 \text{ m/s} )
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Use the average speed to calculate the time for the 700 m race: Time = ( \frac{700 \text{ m}}{4.1737 \text{ m/s}} \approx 167.44 \text{ s} )
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Convert this time back to minutes and seconds: 167 seconds = 2 minutes and 47 seconds.
Therefore, Lara should take approximately 2 minutes 47 seconds to complete a 700 m race.
Step 2
How does this affect your answer to part (a)?
Answer
Since Lara's average speed actually increases the further she goes, it implies that her calculated time of 2 minutes 47 seconds for the 700 m race may be higher than the actual time taken. As she becomes more proficient and faster with increased distance, she would likely complete the race in less time than what was calculated in part (a). Therefore, indicating that her performance would result in a quicker time than derived from a constant speed assumption.