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The team swam a time of 8min 06.16sec, Dunedin's Fairweather swimming the first leg in 1min 57.38sec.
She was followed by former Kavanagh College pupil Carina Doyle, who now lives in Auckland, in a time of 2min 02.18sec.
Eve Thomas and Ali Gayler swam the final two legs.
Australia finished as the clear top-seed for the final in 7min 44.61sec, while the United States was second in 7min 47.57sec.
Hungary's 7min 56.16sec was the slowest qualifying time.
Meanwhile, Lewis Clareburt broke his own New Zealand 200m IM record to qualify third last night to qualify for today's semifinals.
He finished in 1min 57.27sec to knock 0.62sec off his record.
The United States' Michael Andrew was the fastest qualifier in 1min 56.40sec.
The semifinals are scheduled for 3.08pm today (NZ time).