Donald swims 3 lengths of a swimming pool in 93 seconds - OCR - GCSE Maths - Question 1 - 2017 - Paper 1
Question 1
Donald swims 3 lengths of a swimming pool in 93 seconds.
(a) Use this information to show that he could swim 100 lengths in under 55 minutes.
(b) What assumption d... show full transcript
Worked Solution & Example Answer:Donald swims 3 lengths of a swimming pool in 93 seconds - OCR - GCSE Maths - Question 1 - 2017 - Paper 1
Step 1
Use this information to show that he could swim 100 lengths in under 55 minutes.
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Answer
To demonstrate that Donald can swim 100 lengths in under 55 minutes, we first calculate the time it takes for him to swim one length of the pool.
Finding the time for one length:
Donald swims 3 lengths in 93 seconds. Therefore, the time for one length is given by:
extTimeperlength=393extseconds=31extseconds
Finding the time for 100 lengths:
To find the total time for swimming 100 lengths, we multiply the time per length by 100:
Convert seconds to minutes:
Next, we convert 3100 seconds into minutes:
3100extseconds=603100extminutes≈51.67extminutes
Since 51.67 minutes is less than 55 minutes, we conclude that Donald could indeed swim 100 lengths in under 55 minutes.
Step 2
What assumption did you make in part (a)?
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The main assumption made in part (a) is that Donald maintains a consistent pace while swimming each length. This means he will take approximately 31 seconds per length for all 100 lengths, without fatigue or any variations in performance.
Step 3
Suggest one reason why he might not achieve this.
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One reason Donald might not achieve swimming 100 lengths in under 55 minutes is due to fatigue. As he swims more lengths, his energy levels may decrease, causing him to slow down and take longer for each subsequent length.