Dangit.
Dangit dangit DANGIT! How'd this even happen? C'mon, Applejack, there's gotta be a diplomatic solution to this horseapples...
...oh, howdy, partner. Ah, don't mind me...
...what's wrong? Ah, it don't concern ya, ya don't need to know. It'd just put ya in a right pickle if ya did.
...ya wanna listen anyway? Well, if ya say so. So, get this.
It all started when Rarity - ya know, who runs the Carousel Boutique - yeah her, she got this customer who was a right pain in the flank to her. Some fancy too-good-for-his-own-horseshoes type all the way from Canterlot. Rainbow Dash got into a right stew about it, and they had a right big argument right there in front of the shop.
Well, one thing led to another and then Rainbow said, "Well, Ah'll bet Rarity could totally beat ya in a race any day!"
...Ah see that look on yer face. Yeah, it went exactly as well as ya think it did.
That guy - Steady Pace, Ah think his name was, he said that she had that bet, and now Rarity's gonna have to run a marathon against that guy for the fate of the Boutique!
She's crazy! No offense to Rares, but magic don't exactly tone yer muscles much, if ya know what Ah mean. Ah guess Rainbow was real sorry afterwards, sayin' she could do it instead, but Rares insists. Somethin' 'bout how she wouldn't want proxies, and that she'd run that race, for the reputation of the Boutique.
Ah mean, not that Ah don't get behind what she's sayin', but she don't stand a chance. Twilight's actually run some simulations on some fancy machine she's got. That Steady Pace did a lot of charity sports events, and he's got stamina to spare, that guy. Much as he was a jerk, that's the honest truth. Now the way he runs, he could do a mile in eight minutes, no stoppin' for breaks or slowin' down. Guess ya don't get a name like that fer nothin'.
Rares, she ain't too bad in short bursts, but she always has to slow down to catch her breath. She reckons she could swap between gallops and trots to save her energy, but her fastest mile was still a second slower than that Steady fella. And Ah'm not one for fancy mathematics, but a second slower is still slower.
So that's it. Rarity's runnin' a race that Ah don't think she could win. Not without cheatin', and where would that leave her even if she won? Ah don't see a way...
...
...yer kiddin'? Ya actually think Rarity could stand a chance? How? Ya don't have some sort of way to pull a fast one on him, do ya? Cos if ya do, Ah ain't advocatin' it.
...ya don't? So's how's Rarity even supposed to beat that guy and keep her business?
Easy
as you said, rarity sprints then trots, so while her avrage is a second slower, she out paces him while running, so while in 26 miles rarity is 26 seconds behind, she can catch up if her sprint speed is good enough to cover the rest in less than 1 minute and 36 seconds
9230571
Won't accept that answer without the proof this is possible.
9231127
steady pace runs a constant 1mile/8min OR 480 seconds
To cover 26 miles it takes 480×26=12480 seconds or 208 minutes(3hours,28 minutes)
To cover the last .2 miles it takes 480×.2=96 seconds(overall his time is 3h29m36s)
Rarity on the other hand switches between 2 speeds that average 1mile/481 seconds
Lets say it takes 12.016min at her slow speed and 4.016 at her top speed(the average of these 2 speeds is the 8 min 1sec she runs)
As stated before, after 26 miles she is 26 seconds behind, BUT she can cover the last .2 miles in 48 seconds(3h29m14s)
9231270
Not the proof I've got down here.
Think more along the lines of about how Rarity can run at two different speeds, yet cover every mile in the same amount of time.
9231423
But u said she takes an average of 1 second slower
the 12m1s and 4m1s is 16m2s, i took 2 diffrent times so divide by 2, 8m1s
9231432
At no point in the puzzle's summary do I mention averages. I said she runs a mile in eight minutes and a second by running at two different speeds.
Break the guy's kneecaps just before the race starts,
Idea:
Rarity moves at 1 mile/km/unit in 481 seconds, while Steady moves that same distance in 480 seconds. Rarity, however, alternates between a race-car fast pace and a snail pace.
Assuming that she picks up her speed at the beginning of the mile, and drops it later in the mile, she can outrun Steady within that 0.2 mile space added to the end, getting a marginally better time as she catches up to Steady, then drops behind again consistently.
Lets get back to this
9231446
if rarity spends half the mile running 1 of the speeds i list, and the other half on the other speed, its 8m1s to cover a mile, she then does the fast speed for the last .2
9231423
You say here that it takes 2 speed to cover a mile in the same time
HOWEVER
The whole point of this is rarity takes more time to do a mile overall,meaning she hits the 26 mile mark 26 seconds after steady pace, but since rarity changes speed, she can pass and beat steady by doing her faster speed, as proven by the math i showed previously
9252546
The frustrating thing is, you have the right idea, it's the proof that's off.
I'll just scream the proof i'm looking for at you: solve it in terms of algebra.
9252635
Ok then ill convert my answer into algebra
rarity runs 12m1s/mile for X distance
And 4m1s/mile for Y distance, X+Y=26.2 and Y>X good enough?
Without knowing the difference between rarity fast speed and slow speed, and how long she does each make this though
But i think if her fast speed is X times faster than steady and her slow speed is equally slower the steady, then she needs to do the fast speed for X-1/X of each mile, and slow speed for the rest and then do the fast speed for the final .2
I can only guess, that Rarity has to time her speed boost for the eighth minute (or end thereof), so, when Steady Pace began to get tired, she'd have reached her max. speed and given him a headstart. By the end of the eight minutes she'll be late by a second, but she can catch up with it, since Steady Pace's speed would be less, than hers. Who knows?.. she could win.