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.

(a) 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 $35 \mathrm{~m}$.

(b) Find Suzie’s average speed for her swim of 30 lengths.

[5]

(c) Determine whether, exactly 8 minutes after she starts to swim, Suzie is swimming away from or towards her starting point.

[2]

(a) $325 $;

(b) $1.17 \mathrm{~m} / \mathrm{s} $;

(c) away from the starting point

[Maximum marks: 9 marks]

(a)

Total time $=\frac{10}{2}(40+25)=325$

(b)

Total distance $=35 \times 30=1050$

Total time $=325+25 \times 10+\frac{25\left[\left(\frac{40}{25}\right)^{10 / 9}-1\right]}{\left(\frac{40}{25}\right)^{1 / 9}-1}=894.7970999$

Average speed $=\frac{1050}{894.7970999} \approx 1.15 \mathrm{~m} / \mathrm{s}$

(c)

Consider $\frac{8 \times 60-325}{25}=6.2$, this implies that Suzie is on her 17 th lap. Thus she is swimming away from her starting point.