The time, \(t\) hours, for a team of car park attendants to fully clear a stadium car park is inversely proportional to the number of attendants, \(n\), on ...
Question 1 Report
The time, \(t\) hours, for a team of car park attendants to fully clear a stadium car park is inversely proportional to the number of attendants, \(n\), on duty. The curve shows this relationship, passing through the point where \(4\) attendants take \(3\) hours.
- Find the constant \(k\) in \(t = \dfrac{k}{n}\). (1)
- Use your formula to work out how long \(8\) attendants would take. (2)
Answer Details
The curve's label, \(t=\frac{12}{n}\), and the marked point where \(4\) attendants take \(3\) hours both describe the same inverse-proportion relationship: substituting the known pair of values finds the constant \(k\), and the completed formula then predicts the time for any other number of attendants.
- Substituting \(n=4\), \(t=3\) into \(t=\frac{k}{n}\): \[ 3 = \frac{k}{4} \] so \[ k = 12 \] [1 mark]
- With \(n=8\): \[ t = \frac{12}{8} = 1.5 \text{ hours} \] [2 marks]
The curve falls steeply for small numbers of attendants and flattens out for larger ones, which is the typical shape of an inverse-proportion graph: each extra attendant saves less time than the one before, since doubling the attendants from \(4\) to \(8\) only reduces the time from \(3\) hours to \(1.5\) hours, not to zero.
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