The Race Against Time is like a generic plot in almost all of its respects: There’s a problem, and its the good guys’ job to fix it. Once they do, the story is done. However, there is one main difference that differentiates this plot from the rest: there is a time constituent involved.
That “time” element is what inspires the “race”. It is the focus of the whole story: unless the heroes manage to fix the problem before the clock runs down, some very bad things are going to happen. This can take the form of the death of a family member, the demise of someone important, a world cataclysm, several people and/or places being wiped out, and many, many more happenings. But whatever it is, it’s bad.
In a lot of video games, you have a PvE mode and a PvP mode. PvE is Player versus Environment, and PvP is Player versus Player. If the Revenge plot is a “PvP” mode, then The Race Against Time would be a PvE mode. It’s not necessarily the people, but the circumstances that the good guys are working against.
Now, I’m not saying that there can’t be a proper villain in The Race Against Time. However, the main problem is usually something that is caused by the villain, rather than being the villain themselves. This is because one single villain usually doesn’t destroy a city: it’s a bomb, an army, or something we don’t know about.
The true enemy here is time. The villain will do this very evil thing if and only if you don’t solve the mystery in time, pay him the money on time, deliver the hostage on time, foil his plans on time, or anything else on time. If the good guys can beat the clock, nothing bad will happen.
And, of course, in any good race, there should be some roadblocks. Things that get in the way of the heroes’ progressing to victory. If time is the heroes’ enemy, then speed is their closest ally. If you are writing what you believe to be a Race Against Time, focus on the thought that speed is the greatest ally and weapon of the good guys.
Therefore, try to make the villain make obstructions that block the hero’s way. This is for the sake of time and time only: they don’t need to be focused on eliminating the main characters, simply on delaying them. The villain needs to recognize that all they need is time in order to achieve what they want.
Of course, if there’s no set villain, just make the obstructions naturally occurring. However, the obstructions need to at least be there: it causes the most nefarious plot holes otherwise: how bad would it be if the heroes could just rush forward and claim victory, and then didn’t?
Another note about the obstructions: they can be many or few, but they have to be debilitating enough to delay the final resolution. You can have one big one that the entire story is centered around defeating, or a whole bunch of little ones that pop up, each after the other. Either way, they have to be good delaying tactics.
However, probably the most important element of The Race Against Time is the close-cutting end. If the heroes make it to the end with time to spare, it’s obvious that they could have taken time to lounge around lazily and play some video games before going out to save the world. This is ridiculous. If you’re going to create a Race Against Time, cut it close. Make the reader chew their nails vociferously until the final confrontation.
The Race Against Time probably employs the tactic of anticipation more than any other genre of story. The reader feels like they’re by the main characters every step of the way: sweating with them, working with them, worrying with them, and ultimately celebrating with them. Keep this in mind if this is the kind of story you’re writing.
Good luck, and happy writing!