Be patient! Covering a whole city is not easy at all! To extinguish fires more quickly, you need to buy more Fire Trucks by tapping on your Fire Station or upgrade your fire trucks and their items in the UPGRADES section (tools icon at the bottom part of the screen).
Also, don’t forget about the Water Tank of your Firehouse! Water is essential for extinguishing fires, and you can cover more of them by upgrading the Water Tank capacity or its refilling speed. You can also do this by tapping on your Fire Station.
In a more desperate situation, you can x3 the speed or fill the Water Tank immediately by tapping on the helping banners at the right part of your screen once they appear.