The depth of water in a garden pond is 57.8 cm. The depth decreases by 0.3 cm per day. (a) Assume the depth continues to decrease at the same rate. After how many days will the depth reach 54.2 cm? (b) If the depth of water decreases at a slower rate, what effect will this have on your answer to part (a)?

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The depth of water in a garden pond is 57.8 cm - OCR - GCSE Maths - Question 5 - 2018 - Paper 5

Question 5

The depth of water in a garden pond is 57.8 cm. The depth decreases by 0.3 cm per day. (a) Assume the depth continues to decrease at the same rate. After how many d... show full transcript

Worked Solution & Example Answer:The depth of water in a garden pond is 57.8 cm - OCR - GCSE Maths - Question 5 - 2018 - Paper 5

Step 1

Assume the depth continues to decrease at the same rate.

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Answer

To determine how many days it will take for the depth to decrease from 57.8 cm to 54.2 cm, we first calculate the total decrease in depth:

$ext{Total decrease} = 57.8 ext{ cm} - 54.2 ext{ cm} = 3.6 ext{ cm}$

Next, since the depth decreases at a rate of 0.3 cm per day, we can find the number of days by dividing the total decrease by the daily decrease:

$ext{Days} = \frac{3.6 ext{ cm}}{0.3 ext{ cm/day}} = 12 ext{ days}$

Therefore, it will take 12 days for the depth to reach 54.2 cm.

Step 2

If the depth of water decreases at a slower rate, what effect will this have on your answer to part (a)?

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Answer

If the depth decreases at a slower rate, it will take longer for the depth to reach 54.2 cm. The time calculated in part (a) is based on a decrease of 0.3 cm per day; thus, any reduction in the rate of decrease will proportionally increase the number of days required to reach the specified depth.

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