Doing a rough back of the envelope calculation, YSSY is about 4km x 3 km which Mr Pythagoras tells me gives a diagonal of about 5 km. If you accept that the firestation is not too far from the centre of the diagonal the fire tender would have to travel perhaps up to 3 km to get to an incident. To be able to do that inside 180 seconds it would need to achieve an average speed of better than 60 kmh. Allowing for reaction time and acceleration that would seem to be well within the capability of the tenders at YSSY.
Obviously based on a whole lot of mostly unstated assumptions, but it gives a seat of the pants comfort level.
I could also take comfort from the facts given at:
http://www.airsidetarmactours.com/facts.html
Quote:
The Rescue Fire Fighting Service (RFFS) is on call 24 hours per day and is required by international regulations to be capable of reaching an emergency anywhere on the airfield within 3 minutes. The fire tenders at Sydney Airport are constant 6WD and weigh 34 tonnes when full. Each vehicle carries 10,200 litres of water and 1,300 litres of foam mixture. When mixed, this produces around 102,000 litres of fire retardant foam, which can be applied in around 2.5 minutes. Each vehicle was purchased at a cost of around $1.2 million ...
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Compare that to what we had only 60 years ago:
http://www.airwaysmuseum.com/ARFF%20SY%2047-48.htm
And we had a 738 with a blown tyre at YSSY only a couple of years ago:
https://www.pprune.org/archive/index.php/t-283563.html