The north end of the Strip is generally considered to be Sahara Avenue, but since Stratosphere is a mere quarter-mile north of that, we're including it here. From Stratosphere to Mandalay Bay, it's 4.8 miles right down the Strip.
Now, most people in average physical condition can walk a mile in 30 minutes at a comfortable pace and 20 minutes at a brisk pace. But by the time you get to the third and fourth mile, especially on concrete, most people's pace slows a bit. Thus, assuming an easy stride, perfect weather conditions, light crowds on the sidewalks, a straight shot from one end to the other without stopping or taking side trips into casinos, and a 20-minute mile for the first two and a 30-minute mile for the last 2.8, it'll take you just over two hours.
However, in the real world, it never happens this way. You'll have to take small detours to negotiate the pedestrian overpasses at Flamingo and Tropicana. You'll fight crowds the whole way. You'll also, without fail, want to stop and rest, grab a bite or a drink, wander in and out of the big casinos, take pictures, view the Bellagio fountains, pause for your free souvenir photo at Imperial Palace. You'll also get accosted by timeshare salespeople and porn purveyors, blunder into a TV or movie shoot, stumble on some outdoor entertainment, and on and on. So, given the ambient conditions, it can take days to get from one end of the Las Vegas Strip to the other on two feet.
That's why, taking into account the wear and tear on shoes, shins, spine, and sanity, we highly recommend dividing Las Vegas Boulevard South into several sections and touring the north, central, and south Strip at leisure. It helps that they divide into convenient groupings: Stratosphere and Sahara; Circus Circus, Riviera, and Stardust; Fashion Show Mall, Frontier, and Wynn Las Vegas; TI, Mirage, Caesars Palace, Barbary Coast, Flamingo, Imperial Palace, Harrah's, Venetian; Bellagio, Bally's, Paris, Aladdin; Monte Carlo, New York-New York, MGM Grand, Hooters; and Tropicana, Excalibur, Luxor, Mandalay Bay.
You can ride the Strip Trolley, which pulls up to the front door of the casinos, from group to group, or you can do a circle, return to your car, and drive from one group to the next. You can also, of course, go on the forced march that your question might imply. However, to catch all the sights in between, plan on three full days or nights walking from Stratosphere to Mandalay Bay.
