With Build 1.1.138, pushed live on July 23, 2013, Disruptor Beam introduced a new Speedup UI. This UI greatly streamlines the way you can speedup items, upgrades, and quests that are underway. You may view the new speedup in the attached image, new_speedup_ui.png.
The way the new UI works is by providing a single-click action that lets you speed up your action by using the speedup that best fits your action. For example, if you are producing an item and it takes two hours to complete, the game will choose a two-hour speedup for you. If you are producing an item that takes thirty minutes, a thirty-minute speedup will be chosen.
Sometimes, you may wish to use your own speedup items to speedup your production or quest, which may not match what the game chooses. In that case, you may click on the speedup item icon to choose a speedup from your inventory. If you do not have a speedup in your inventory, the icon will not show up. You may see which icon to click in the attached image, use_different_speedup.png.
If you do not have an item, then an amount of gold will be subtracted equal to the cost of purchasing a speedup. If the amount of time you are speeding up is longer than the maximum speedup item time - currently set at 28 hours - then the gold cost will smoothly scale up to however much is required for that item.