In DC's TV-series (and comics), Barry Allen is The Flash: a superhero powered by the speed-force. This speed-force allows him to move incredibly fast, can be transferred to others, and there also exists a synthetic version of it (it's not that healthy).
Given current technology levels, how far you can push a real human being? Where are the limits for an enhanced human? How fast could he run? What would stop him from running any faster? What would some other side effects be?
Imagine you have unlimited resources (but you can't make up anything, everything has to be announced or existing in our current world) and labor. You can pump him (or her) full of drugs if need be.
I know, a person won't be able to run at supersonic speed, but how fast could one actually go? 60 mph perhaps?
What would be the most effective way or Drug combination to accelerate a Human being to maximum possible speed. In other words: How to create Velocity 9? And How fast would that be?
The Flash is a supernatural (and made-up) entity, which cannot be replicated by science in any way, shape, or form. However, pushing people to simply run faster is, of course, possible, depending on what you're trying to accomplish, and price you're willing to pay (or rather the price your test subjects are willing to pay).
Consider that the current world men's record for sprinting 100 meters (held by Bolt), is essentially 23.35 miles/hr. That is the fastest that a talented, and highly trained human being has ever been ever to run (that we know of).
He did this at the peak of his physical performance, although not on any performance enhancing drugs (we hope). And so, right off the bat, you're opening the door to potentially having him run faster if he did partake of some of those drugs.
However, everything has consequences. Running that fast will take a heavy toll on most people. They will most likely tear muscles and ligaments achieving higher speeds, because the human body has certain limitations. And they will still come nowhere near 60 mph. In fact, most would be lucky to reach Bolt's speeds while not on drugs.
Also consider that many professional athletes develop a wide range of injuries related to constantly training, and performing to the limits of their physical ability. The people enhanced in this manner would likely suffer terrible injury much, much sooner in their "careers". Most likely such an enhanced person would maybe have a career measured in a few tens of kilometers, not years.
What you might try is a combination of drugs which enhance blood oxygenation (which is what Armstrong was taking to stay at the top of the bicycling competitive world), and maybe replacing people's legs with prostheses along the lines of the Blade Runner.
Alternatively, the world's militaries are currently developing powered exoskeletons. These things are primarily meant to enable troops to carry large weights. They're currently nowhere near what we see depicted in movies, or video games, however in a few short years they may well get there. These things may very well allow a human being to move very freakin' fast. Maybe not sustain a 60 mph sprint, but certainly move at Bolt's speeds for short periods of time without having to be anywhere near as highly trained as him.
So, this equation pretty much defines speed (Indicated here by Velocity (V)) and the energy it takes to get to that speed (E) for a person of a certain mass.
As velocity is generally taken in m/s (metres per second) we'll have to convert your 60mph into m/s
$60mph*1.6$ (miles to kilos)$ = 96kph$
$(96kph/3600)*1000$ (1km to 1000m) $ = 26.67m/s$ (2 d.p)
Now you can plug that back into the equation above to determine how much energy you'd need to get to those kinds of speeds, I'm not going to do it for you, but I will move on a little bit to how fast humans can go currently.
Usain Bolt; the fastest person in the world; currently only clocks in at a paltry $12.4 m/s$ but that's only for a very limited time (the last 2.4 seconds of his 100m dash).
Compare that to the cheetah's $26.67m/s$, which meets your requirement, but can run for up to 60 seconds and the American Antelope's $24.59m/s$ over an incredible $6km$ (it can increase its speed up to an eye-watering $39.56m/s$ for a short burst ($0.8km$)
Even these speeds are nothing compared with the Peregrine Falcon; which, in a stoop can reach speeds of $108.18m/s$ ($242 mph$ / $389kph$)
(All these facts can be checked over at: Wikipedia as the tag hard-science has just been added)
So what does this mean for our humans? Well it means that the kind of speeds you're looking for are technically plausible, as they currently exist in other animals, but whether or not it is possible to give human beings this kind of speed is debatable.
We don't currently have the technology to splice animal DNA into our own and there's no indicators of it happening any time in the future; so I think the answer fully if you've read this far is: