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O'Connor hung on to the coat-tails of China in fourth during the first 200m, while Carlin was able to keep Britain in contention at the midway point.
Sweden edged ahead of the United States, while Turner for GB battled it out with China in the third leg of the showdown.
Miley was sent in to anchor, but she failed to hang on to the bronze-medal position and missed out in fifth place, while Sweden dropped behind to finish fourth.
Italy and China took silver and bronze respectively as the USA posted a winning time of 7:45.37.