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Rowan’s bath has a hot tap and a cold tap - OCR - GCSE Maths - Question 7 - 2021 - Paper 3

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Rowan’s bath has a hot tap and a cold tap. When turned on full, each tap on its own will fill the bath in 6 minutes. Rowan turns both taps on full. How long will it... show full transcript

Worked Solution & Example Answer:Rowan’s bath has a hot tap and a cold tap - OCR - GCSE Maths - Question 7 - 2021 - Paper 3

Step 1

Calculate the rate for each tap

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Answer

Each tap can fill the bath in 6 minutes, meaning the rate of each tap is:

  • Hot tap: 1 bath / 6 minutes = ( \frac{1}{6} ) baths per minute.
  • Cold tap: 1 bath / 6 minutes = ( \frac{1}{6} ) baths per minute.

Step 2

Determine the combined rate of both taps

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Answer

When both taps are turned on, their combined rate is:

[ \text{Combined rate} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \text{ baths per minute} ]

Step 3

Calculate the time to fill the bath

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Answer

To find the time it takes to fill one bath at the combined rate, we can use the formula:

[ \text{Time} = \frac{1 \text{ bath}}{\frac{1}{3} \text{ baths per minute}} = 3 \text{ minutes} ]

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