N2021 P2 Q4

Mrs Wong is the president of a swimming club. She devises a training programme for members of the club. Members swim \(10\) lengths of a swimming pool; the time taken to swim the first length is \(40\) seconds and the time taken to swim the last length is \(25\) seconds. The times taken for each of the \(10\) lengths are in arithmetic progression.

1. Find the total time taken to swim \(10\) lengths using Mrs Wong’s programme.[2]

One of the members of the club, Alfie, devises a different training programme. In Alfie’s programme the time taken to swim the first length is \(25\) seconds and the time taken to swim the last length is \(40\) seconds. The times taken for each of the \(10\) lengths are in geometric progression.

Suzie swims \(30\) lengths. She swims \(10\) lengths using Mrs Wong’s programme, then she swims \(10\) lengths taking \(25\) seconds for each length, and then she swims \(10\) lengths using Alfie’s programme. The length of the pool is \(35\text{ m}\).

2. Find Suzie’s average speed for her swim of \(30\) lengths.[5]
3. Determine whether, exactly \(8\) minutes after she starts to swim, Suzie is swimming away from or towards her starting point.[2]