Pinkie Pi
This story takes place in an alternate world where Pinkie and Twilight have opposite brains. In this alternate dimension, this takes place before Twilight as we know her became a princess. I hope you enjoy!
The pink pony walked in small circles around the laboratory in her basement. This just doesn't make any sense. If one team of pony workers can complete a job in a total of 9 days, and the second team can complete the same job in 7 days, and if the first team worked for three days, and then the second team joined in... how many days was the job completed? Pinkie Pi thought to herself.
Her unicorn friend Twilight Sparkler became really confused, and was having some trouble with her math. She knew that her magical friend Pinkie would help her.
"Did you find it yet? Do you know what the answer is?" The purple unicorn asked, rocking side to side in a wooden stool.
Instead of answering, Pinkie put on her thick, light blue glasses. Trotting over to her long chalkboard, she immediately began drawing out pictures.
"What's that?" The unicorn asked, jumping off the stool. Now bouncing up and down, she leaped over beside Pinkie. Her big, purple eyes was focused on the drawing of circles and lines on the board, along with a few scribble-looking things.
"What's that thing?" Twilight asked, pointing to an equal sign with a slash through it.
"It's an nonequivalent sign. Did you know that there are about 12 nonequivalent hydrogens in lauric acid?" Pinkie Pi replied, keeping her expression serious as she wrote.
"Oh. What does that mean?" Twilight Sparkler asked, now even more confused than earlier.
"Lauric acid, or also known as systematically dodecanoic acid, is the saturated fat acid with a 12-carbon atom chain, thus falling into the medium chain of fat acids, creating a white, powdery solid with a faint odor of bay oil or soap." Pinkie Pi answered, continuing to draw out the math problem.
"Oooh! And what does that mean?" Twilight asked, a smile still glued to her face.
Pinkie sighed. "You'll learn someday. For now, let's just answer your math problem."
"Alrightie!" Twilight bounced up and down, but unlike when most ponies make a 'thud' noise every time they hit the ground, she barely made a sound. Her eyes stayed on her pink earth pony friend as she began to work out the problem.
"Okay, Twilight. If the first team completed 1/3 of the job working alone for 3 days. That leaves 2/3 of the job remaining, correct?" Pinkie Pi asked rhetorically, her eyes still on the math problem in front of her.
"Uhh... whatever you say!" Twilight continued bouncing.
"So, if I take the 2/3 and rewrite that as a fraction with 9 and 7 days to represent the number of days they supposedly worked..." Pinkie trailed off in into genius talk. Her friend Twilight Sparkler bounced around. The purple unicorn was very interested in the earth pony's lab, even though she came down into this weird room a lot. All around her weird machines beeped and buzzed. Lights flashed on and off. Chalk scratched on the chalkboard. Graphs hung like posters on the wall, and many instruments as big as telescopes down to the smallest microscopes could be found wherever you looked.
Pinkie Pi wrote an new equation on the board. "So, if (1/9) x + (1/7)x = 2/3, then 7x + 9x = (2/3), and then if I have (63)..." Pinkie began mumbling as she wrote.
"Hey! I just had an idea!" Twilight shouted.
"Twilight Sparkler! Hush! I'm trying to work!" Pi said.
"Sorry... hey, can I ask you about it later?" Sparkler asked.
"Yeah, sure. But now, I am doing a math problem. Your math problem." Pinkie Pi continued to draw.
Twilight Sparkler sat down. Her hoof tapped the cold, hard, wooden floor quickly as she waited for her friend to be done.
"Ah-ha! 16x = 42, so if x = 2.625 days, then that means... the total amount of days is 5.625! Ah ha!" Pinkie Pi exclaimed, circling the answer on the now messy looking chalkboard.
"What?" Twilight asked.
"Your answer is 6, Twilight. 6." Pinkie said.
"Oh! Okay. Thanks, Pinkie!" The purple unicorn said. She began walking onto the staircase leading out of the basement.
Twilight Sparkler was about to exit when she remembered she wanted to ask her friend something. "Uh... Pinkie? Can I ask you now?" the unicorn asked.
"Sure. What?" Pinkie replied, cleaning off the chalkboard.
"What if in an alternate dimension somewhere, oh, I don't know... you and I had somehow swapped personalities, and I was smart and you were whatever I am, and if I also at the same time was a princess with wings?"
"I doubt that's possible." Pinkie rolled her eyes.
"Are you sure? I mean, you did this math and all... I don't know. To me, traveling intergalactic dimensions to an opposite world seems easier to me than algebra." The purple pony left the room.
Pinkie sighed. If I was ever as hyped as that pony...
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PFFFT!!! PFFHAHAHAHAH LOL!
As a heads up, the answer is actually 6 days, if they still have .625 of a days work to do the job isn't complete.
Other than that, interesting concept and execution.
I just set it as a proportion: 7/9=?/3. 7/3 is 2 and 1/3 so add that to the 3 days already done, and you get 5 and 1/3 days, so it took them 6 days.
I actually don't know how the commenter on that website found the answer! I don't understand some of the work he showed. Here is how I did it.
Let's call the job J. J = 9A = 7B, A referring to team one's speed and B referring to team two's speed.
Team one worked for three days, so the remaining job is 6A.
The amount of time it will take both teams together to complete the remaining work can be stated as:
6A = X(A+B)
We also know that 9A = 7B, so B is equal to 9A/7. Thus,
6A = X(A+A*9/7) = X(A*16/7)
42A = 16XA
42 = 16X
42/16 = X
2.625
Add in the three days team A worked for, and you get 5.625.
HA! Hilarious! I love how Twilight knows about the 'other' Twilight and Pinkie, and I bet Pinkie Pie knows about her, too! XD And the name 'Pi' for the smart Pinkie, very clever!
Paradise Oasis
Historian mare of Dream Valley
What possible purpose could "Sparkler" have for needing to know the answer to that math problem?
Comment chain: what would your cutie mark be if you were a pony?
Mine would be the pi symbol, made of all the numbers of pi (3.1415926535897932384626...)
A mare may dream, Pinkie Pi (not to be confused with Pinkie Pie, a completely different pony!).
...OK... I'm doney with the funny.
On to verify the Maths problem!!! Because we must! And we do what we must, because we can!
Ahem!
Team one completes job in 9 days;
Team two ~ ~ ~ 7 days;
T1 does a ninth a day;
T2 does a seventh a day;
Working together at the same speed, they supposedly do a ninth + a seventh, which equals 9 + 7 (7 × 9)-ths, which is 16 63-rds, or 16 / 63, which is a tad > 16 / 64, which equals 2^4 / 2^8, = 2^(4-8), = 1 / 2^4, = 1 / 16;
(Must have miscalculated. Inexcusable!)
16 / 64 = 2^4 / 2^6 = 2^-2 = 1 / 4;
Thus T1 + T2 do a fourth a day (times 64 / 63, meaning, plus 1 / 63 times 1 / 4);
T1 has worked 3 days, thus completing 3 / 9 of job, which is a third thereof;
Conveniently enough, a third is 21 / 63;
Meaning, the two teams together have to complete (63 - 21) / 63 of the job;
I. e. 42 / 63 thereof;
Divide 42 (63-rds of job left) by 16 (63-rds done daily);
Get 6 × 7 / 16 = 3 × 7 / 8 = 21 / 8 = 2 + 5 / 8 more days (to complete the remaining 2 / 3);
The first 1 / 3 they've done in three days;
Answer: they'll complete their job in the manner described in 5 full work days plus 5 / 8 of a work day;
.
Meaning, 6 work days sans 3 / 8 thereof;
Meaning, they get an early leave on the sixth day. Might want to cut expenses and not to pay them for the full sixth day