Solution:
Given their relative speeds, and Big Macintosh's break times, Applejack catches up to Big Macintosh at the 1 1/2 hour, 3 hour, 4 1/2 hour, and 6 hour marks.Big Macintosh took breaks at the 1 hour, 2 1/2 hour, and 4 hour marks respectively, and finished after 5 1/2 hours -- exactly 1/2 hour before Applejack.
Either way, they both worked very hard and deserve a bit of a break, don't you think?
Spike grinned as he laid out the explanation for Applejack, with Twilight nodding her approval as he spoke. "So you see," he said at last, "if you're finished now, that means Big Macintosh has to have finished his, too!"
"Well, all right," Applejack said grudgingly. "If'n yer sure."
Twilight nodded. "He's right, A.J.," she said. "Well done, Spike!"
"Well," Spike said, "I can't be your Number-One Assistant without picking up a few things."
"In that case," A.J. said, "what brings y'all down here again?"
"Princess Twilight is... concerned," Rarity said.
"Oh, come on, Rarity," Twilight objected. "I'm sure you've noticed the way everypony can't get anything done today. Everywhere we go, there's a puzzle, riddle, or conundrum for us to solve, and nopony seems to be able to do anything about them until Spike and I solve them!"
"Well, shoot," Applejack said, "y'all must be happier'n a pig in th' mud!"
Twilight blinked, confused. "Why would that make me happy?"
"Well," said Rarity, "everybody wants to feel useful..."
"And ya gotta love puttin' all o' them smarts ta good use."
Twilight grimaced in frustration. "Okay," she said, "yes, I do love riddles. And it is nice to feel needed. But there's a difference between feeling needed and being the one and only pony who can solve everypony's problems for them!"
She had started pacing back and forth in longer and longer arcs as she spoke, and by this point in their conversation had ended up outside the barn. Granny Smith sat contentedly in a rocking chair in the barn, next to a model of the Sweet Apple Acres farmhouse. She looked up from her knitting, frowning, then grinned cheerfully at Twilight and her friends. "Well, howdy there, Twilight!"
"Look!" said Twilight, gesturing at Granny Smith. "You can't tell me that's normal behavior!"
Applejack frowned, looking back and forth between her grandmother and her friend. "Um, Twi...? She's knittin'. She does that."
"But... the little farmhouse! Inside the barn!" Twilight jabbed a hoof at the offending structure. "What's that all about?"
"Well," Applejack said. "Ah'm just plain, ordinary folks, but Ah reckon we could just... ask her?"
"Fine," said Twilight. "Fine." She trotted up to Granny Smith, her literally ruffled feathers smoothing themselves as she composed herself. "Granny Smith," she called out cheerfully -- a bit too cheerfully, Spike thought -- "do you have any problems, puzzles, or conundrums that I, as a good family friend, can help you with?"
"Nope!" Granny Smith replied cheerfully.
"None?"
"Not a one!"
"Then... what's with the little farmhouse inside your barn?"
"Well, Ah figger unsolved riddles need a home, too," the wrinkled old mare replied. "An' we got plenty o' room here at Sweet Apple Acres, so Ah had Applebloom build a little house fer 'em an' put it in th' barn."
Granny Smith's Riddle Shack
Some riddles may get skipped in the course of Twilight's adventure. After some events, these riddles will be placed in Granny Smith's Riddle Shack. After the story's conclusion, they will be made available in a single chapter, and their solutions added in a separate chapter. At any point in the story, however, the Riddle Shack may be visited in order to view any skipped riddles before the conclusion of the story.
"Riddles," Twilight said flatly.
"Well, Riddles need love, too!" Granny Smith replied.
"I'm not saying I don't like riddles," Twilight said, "I love riddles! Really!" She took a step forward, her wings flaring dramatically. "In fact, I will ensure that no riddle goes unsolved! Sorry to waste your time, Granny Smith, but that Riddle Shack of yours is going to stay empty, or my name isn't Twilight Sparkle!"
"That's the spirit, young 'un!"
Twilight trotted purposefully out of the barn. "Come on, girls!" she called to her friends, "we've got riddles to solve!"
"Wait, your name isn't Twilight Sparkle?" Spike asked, one claw upraised inquiringly.
"Her name isn't Twilight Sparkle?" Rarity blinked in confusion at Spike.
"Ah thought her name was Twilight Sparkle."
Twilight stopped, staring back at the trio. "Are you coming, or not?"
"Where to, Twilight Sparkle?" Spike asked. "If that is your name."
"That is my name, Spike!"
"But you just said..."
"It's a figure of speech!"
"Hold up, now, pardners," Applejack cut in. "This could go on all day if'n ya don't rein yerselves in. Where to?"
"Well, the most efficient path would be to start from one location and proceed in an outward spiral until we're sure we've covered the entire town. Also, that would help us retrieve all of the missing pieces of Princess Celestia's letter."
"Speaking of which," Spike said, "I found a few more pieces!"
"That's my Number One Assistant! Put them with the others, Spike!"
"Done and done! Where to?"
"Well, the next nearest location would have to be the Cutie Mark Crusaders' clubhouse," Applejack said.
"Oooh, I dread the thought of what sort of hijinx they could have gotten up to," Rarity put in. "Shall we, then?"
Twilight grinned at her friends. With them along, this wouldn't be nearly the chore it had seemed earlier. It might even be... dare she think it? ...fun.
* * * * *
They approached the clubhouse at a cheerful canter, Twilight and Spike bringing the other two up to speed on their adventure so far.
"Oh, my," Rarity said, "that is peculiar."
"Ah can't imagine R.D. not knowin' how ta put her clouds in storage. 'Specially since it's somethin' she's so proud of."
"What's that?" Twilight frowned.
"When she first come ta Ponyville, they was so disorganized they lost clouds all the time. Rainbow Dash was the one what figured out how ta put the clouds up so's they wouldn't mess each other up in th' first place."
"How could she possibly forget a system she devised?!" Twilight shook her head in consternation.
"I'm beginning to suspect," Rarity said slowly, "you may be right about there being some kind of spell over Ponyville."
"Well, the more of these riddles we solve, the more information we have to fix this mess," Twilight said. With that, she turned her attention to the clubhouse. As if on cue, an argument broke out inside the treehouse. Three high-pitched voices yelled at each other in a cacophonous mishmash of overlapping words.
"I'M NOT STUPID, YOU'RE STUPID!"
"Scootaloo," Spike identified the voice.
"NUH-UH! THAT'LL NEVER WORK! YOU'RE STUPID!"
Applejack sighed, rubbing the bridge of her muzzle. "Applebloom," she said.
"Well," Rarity put in, "at least--"
A third voice, louder than the other two put together shrieked, "YOU'RE BOTH STUPID!"
"You were sayin', Sugarcube?"
Rarity gritted her teeth. "I was saying that at least my sweet-natured little sister isn't adding her own prodigious vocal talents to the argument, but I was clearly mistaken," she said coldly.
The three adult ponies (and one baby dragon) galloped (and scrambled) up to the entrance of the clubhouse.
"Whoa up, there girls," Applejack yelled, but the Crusaders' argument had gotten physical. Tails were yanked, ears were pulled, and soon the girls were lost in a cloud of dust and frenetic activity.
"Now, Sweetie," Rarity chided, but the Crusaders took no notice.
"Girls!" Twilight yelled, and yet the fight continued. Frustrated, she put a hoof down, hard, and reached out with her magic to separate the fighting fillies. As soon as she did so, the three looked at her, their heads hung in shame.
"Sorry, Twilight," they said in unison.
"That's all right," Twilight said, putting them down. "Now... what's this all about?"
"Scootaloo--" Applebloom began, jabbing a hoof at the offending filly.
"Hey!" Scootaloo yelled, immediately flaring her wings in anger, "that's not fair! You told me to come up with a schedule--"
"Nopony even asked me what I--" Sweetie Belle interrupted, her own argument drowned out by Applebloom.
"You can't even do that right!" Applebloom yelled at Scootaloo, crouching in preparation for another fight.
"GIRLS!"
"Sorry, Twilight."
"Now," Twilight said, "One at a time, what seems to be the problem? Scootaloo?"
"Applebloom told me to come up with a schedule for today."
Twilight nodded approvingly. "It's always a good idea to plan things ahead of time," she said. "That way you make the best use of your time."
"So long as you don't mind spending time planning things instead of doing them," muttered Spike.
"So... what's the problem, then? Applebloom?"
"Scootaloo's schedule is dumb," Applebloom countered.
"Is not!"
"Is too!"
"Girls!" Twilight was losing her cool. She didn't know how Applejack and Rarity could cope with the Cutie Mark Crusaders. (There was no secret to it. Applejack and Rarity simply did their best to keep the damage to a minimum and waited for the storm to pass.) "Why don't you just let me take a look at this schedule?"
"Here," said Scootaloo, proudly hoofing over the paper she'd written it down on.
"Ah," said Twilight, as she examined the paper. "Ah. I see the problem. Spike?" She levitated the schedule over to the baby dragon. "What do you think?"
Puzzle 11
Dumb Schedule!
40/40 BitsScootaloo is clearly upset. She had a whole day of fun and games planned for the Cutie Mark Crusaders, but Apple Bloom took one look at the schedule and said it was dumb.
What part of the schedule did Apple Bloom have a problem with?
