The total time, \(T\) minutes, for an athlete to complete a sports day circuit is given by \(T = 4s + 2h\), where \(s\) is the number of running stations an...
Question 1 Report
The total time, \(T\) minutes, for an athlete to complete a sports day circuit is given by \(T = 4s + 2h\), where \(s\) is the number of running stations and \(h\) is the number of hurdles.
- Work out \(T\) when \(s = 6\) and \(h = 3\). (2)
- Write down what \(2h\) represents in this formula. (1)
- Make \(h\) the subject of the formula. (2)
Answer Details
(a) Substituting \(s = 6\) and \(h = 3\) into \(T = 4s + 2h\) gives \(T = 4(6) + 2(3) = 24 + 6 = 30\) minutes [2 marks].
(b) In the formula, \(2h\) is the part of the total time contributed by the hurdles: it represents the total time added by the hurdles, at 2 minutes for each of the \(h\) hurdles [1 mark].
(c) Subtracting \(4s\) from both sides of \(T = 4s + 2h\) gives \(T - 4s = 2h\) [1 mark], and dividing both sides by 2 gives \(h = \frac{T - 4s}{2}\) [1 mark].
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