The answer to this question appears to be "quite a lot" if you are Doctor Who and the afternoon in question is Monday 16 July 1966. Even though the 16 July in 1966 was actually a Saturday.
This sort of thing happens a lot with a time machine – Rose Tyler manages to take in the Autons, the End of the World and the Gelth between meals before Dr Who's wonky navigation lands her a year into her own future, but for a REALLY classy example of TIME MANAGEMENT you have to travel back to the 1960s.
First on the scene is Dr Who number one, Mr Billy, saving the world from WOTAN: the Will Operated Transistor Apparatus for Naughtiness. Or something. Wicked WOTAN constructed the wind-up WAR MACHINES, in readiness for "C-Day" or "Computer Day", which would be that 16 July that I mentioned. That was when all the computers in the world would be linked up in some kind of world wide network… what a FANTASY!
Meanwhile, over at Gatport Airwick… here's Dr Who number two, Mr Pat the Mighty Trout, landing on the runway only to discover that Mr Balloon is up to no good with his CHAMELEON AIRWAYS, kidnapping the youth of Britain so that his faceless minions could replace them. Ooooh SHUDDER!
Anyway, that's when things REALLY start to get busy.
While Dr Who is putting paid to the plans of THE FACELESS ONES, those evil pepperpots, The Daleks are making off with his TARDIS! It's all part of a plot to lure Dr Who and his best friend JAMIE into their clutches. Drawn to a rendezvous at the EMPORIUM of FAKE ANTIQUARIAN Mr Edward Waterfield, Dr Who and Jamie are knocked out… and when they wake up they have been kidnapped through time to 1866.
But here's the thing – we do not know how much time passes for them… so it could still be THE SAME DAY as far as they're concerned! Talk about JET LAG!
They meet their host, Mr Theodore Maxtible, and are introduced to Mr Waterfield at last learning from him that the house is in the power of the Daleks (not in "The Power of the Daleks", that's a DIFFERENT story). Mr Waterfield's daughter VICTORIA is being held hostage. When night comes around, Jamie goes off to rescue her.
So these events have probably been going on for about a day, now, although the only nap that Dr Who seems to have taken was under the influence of knockout gas. Sleep is for tortoises, though, as he will later say.
During the night, Jamie battles Daleks and booby traps and a mighty Turkish manservant called Kemel to reach Miss Victoria, unaware that this is all part of the EVIL of the Daleks' scheme. They are forcing Dr Who to stay up past his bedtime in order to record Jamie's adventure – in order, they claim, to discover the secret of the "human factor", the reason that they are always defeated.
Once they have what they want, the Daleks bundle everyone off to their home planet of Skaro via a space time tunnel in Mr Maxtible's cabinet of mirrors. So it is still the same day for them when they get there. Even if it is a different day according to the calendar.
Once on Skaro, the Doctor has time to take in a couple of audiences with the Emperor of the Daleks while fermenting a Dalek civil war between times… so about AN AFTERNOON'S work for him.
Even though that is the end of their adventures for that year, the next story begins straight after with Miss Victoria's first entrance into the TARDIS where she is amazed by the console. Ever the show off, Dr Who sets them in flight and they whiz off to Telos and "The Tomb of the Cybermen" where they will encounter the Cybermen. In a tomb.
It is always difficult to know just how long trips in the TARDIS actually take. When he is Paul McGann, Dr Who says it would take ten minutes to get to the other side of the galaxy, but sometimes it seems like it might take days to get anywhere. Anyway, we can tell that it takes at least long enough for Miss Victoria to get changed into a new dress – but not long enough for her to get used to the idea of wearing it. So it might be longer than an hour, but probably less than a morning.
They spend the rest of the day defrosting and refrosting the Cybermen before electrocuting the Cyber Controller, locking up and leaving again. Nice to leave things tidy.
The next story after that begins with Jamie complaining that they have just materialised further down the same mountain, implying that it follows straight on again. Dr Who puts him right, of course: they are in TIBET and have arrived in time for an afternoon being chased around by the cuddly "ABOMINABLE SNOWMEN". The travellers get to spend the night in the Det Sen Monastery – FINALLY some sleep! – before knocking off the Intelligence behind the Yeti the following day.
This is followed by an adventure that ALSO begins with Jamie complaining that they have just materialised further down the same mountain, so AGAIN it appears to be straight after the last one. This time they find themselves at Britannicus Base, below a glacier, where Leader Clent and his men have just dug up a party of ICE WARRIORS. They have to march up to the glacier where the Warriors' ship is frozen and back down to the Base a couple of times, which might take a while, but there's nothing to suggest that they waste more than a day before Varga and his crew get exploded and our heroes slip out the back door again.
All of which means that Miss Victoria first four adventures all-in-all seem to take about three to five days. No wonder she's starting to have a NERVOUS BREAKDOWN by now!
After all THAT, it's probably nearly a REST CURE when Dr Who takes on the SUSPICIOUSLY FAMILIAR looking "Enemy of the World". We do not know if the adventure follows straight on, so they might have had time for a HOLIDAY. Or some of those "Missing Adventure" books. Or at least forty winks. And also, what with all of its JAMES BOND style globe trotting, the story might in fact last for several days or even weeks! Which is positively LANGUID by their recent standards!
Never mind, it'll be rush, rush, rush again soon: a couple of hours to get acquainted with Colonel Lethbridge-Stewart and the London Underground and re-acquainted with the Yetis and a day down on the beach dealing with some very cross SEAWEED.
If the stories had carried on at that breakneck pace then the real mystery would be why Dr Who and Jamie are so upset when Miss Victoria takes the first opportunity to get off the TARDIS when it comes to "Fury from the Deep". After all, if it wasn't for "The Enemy of the World" they would seem to have only known her for about a FORTNIGHT!
So there you are – you should be able to defeat a disembodied intelligence, thwart four alien invasions and unplug at least one mad computer between a picnic lunch and jam and scones for tea.
And if you don't, well you're just not really trying, are you!