With the Formula 1 Singapore Grand Prix just over, people around Miss Loi are apparently still in a “Fast ‘n’ Furious” mood.

So it didn’t seem coincidental at all when Miss Loi got a call from her *tiong chia* (*ala* car modification) cousin from KL (Kuala Lumpur).

Oi Leng Lui! 这个礼拜雪邦那里有的去赛车。一起去要不要？几够力一下喔！

*translated*: “Hey Miss Loi! There’s an auto racing track day at Sepang this week. Shall we go together? Should be fun!”

Not passing up this once-in-a-lifetime opportunity to test out her car’s new intake, exhaust, rims and brake pads, and recognizing there’s NO WAY test them (legally) on Singapore’s roads (nope not even on Singapore’s F1 ‘track’), she quickly agreed and headed to meet her cousin 280 km away at the next-nearest official F1 track – the world-famous Sepang International Circuit!

Where several kilometres of 15 scintillating turns lie in wait to challenge the boldest of all *Ah Beng tiong chia kias* and racer wannabes.

She soon found herself wandering along the pit area, where her senses were quickly overloaded as she came face-to-face with rare exotic sports cars of all shapes and sizes (and engine loudness).

Cars like these Sleek Lotuses …

The ubiquitous Honda Type Rs with their special R-Formula…

Porsches …

And even a flamin’ Lamborghini!

But when she got to these two fierce-looking WRXs however, a familiar voice boomed out across the pits, to her horror …

Miss Loi! What are you doing here?!!!

It was her Japanese Project A bosses – the Takahashi Brothers!

How … how come the both of you are here? Where are your RX-7s???

Speaking through a translator who was present with them,

We are here to test our new WRXs. How dare you sneak out here without our knowledge! You must be severely punished for this!

No! Please forgive me! I’m here because I need a break from all the non-teaching duties I’ve been given! I’m a maths tutor not a MOE teacher!

pleaded a desperate Miss Loi, upon which younger brother Keisuke whispered something in Ryôsuke’s ear.

Well … since you’re already here … let’s have a little race. I will let you off this time if you can overtake the both of us before the track closes for the day.

Miss Loi had no choice. And thus without further ado, they hopped into their respective cars, donned their helmets …

Filled the afternoon air with eager roars of their engines as they lined up and revved in anticipation …

… of a race where no Sexy Maths Tutor had raced before.

Predictably, the Takahashi Brothers pulled ahead right from the start, leaving Miss Loi trailing in their smoke as the monster WRXs disappeared swiftly into the distance.

To make matters worse, other cars were also zooming past her left, right and centre throughout the next couple of laps – as if she wasn’t there:

It was over before it even began, and a disconsolate Miss Loi limped her car around the track – resigned to whatever inhumane punishment that awaits her when she gets back to Singapore.

不是吧？Leng Lui 这么快就放弃了？你经常跟我说你怎么教你学生在考试里就算题目多么难也不得放弃！一定要尽力做下去。拿几分也好过交白卷！

*translated*: “Miss Loi are you giving up?! I thought you always teach your students NEVER GIVE UP no matter how difficult the questions in the exam appear to be? It’s better to score a few marks than hand up a blank piece of paper!”

It was her KL cousin speaking to her from the walkie talkie, having driven alongside her car on the track.

跟我来！让我这个大马车神教教你！

*translated*: “Follow me! And learn from the Car God of Malaysia!”

And so in what was an intensive Last-Minute Buddha Foot Hugging Jφss Sticks Session on track driving, Miss Loi followed her cousin’s car around the track, listening carefully and trying her utmost to follow his instructions that was bellowed through the walkie-talkie set.

After several hair-raising incidents when she doubted if she’ll ever make it back to Singapore to conduct her own Jφss Sticks Sessions, Miss Loi slowly but surely gained a measure of control of her car – like a rider taming a wild horse.

Soon she was feeling at one with the machine, flying through the track at speeds unheard of on Singapore’s roads (at least to her), emboldened by the comforting fact that there WON’T be a traffic police car lurking around the next bend, or a sneaky traffic warden snapping away behind some bushes.

Meanwhile the Takahashi Brothers, being many miles and laps ahead of her and confident that victory was in the bag, began to ease off and turned part of their attention to discuss (through their walkie-talkies) what punishment Miss Loi should receive when they get back to Singapore …

At this juncture, the Takahashi Brothers are lapping at a leisurely pace of 4 minutes per lap. They are 10 laps ahead of Miss Loi and are side by side with Miss Loi at the start of a new lap.

The following is Miss Loi’s speed-time graph for a *single* lap (Note: all acceleration and deceleration are *linear*, and readings are to be read off to the nearest __half__ graphical unit):

Assuming that the Takahashi Brothers’ and Miss Loi’s respective lap times remain unchanged for all laps henceforth, use the appropriate information from the graph to determine if Miss Loi is able to overtake the brothers if there are 90 minutes left before the track closes.

* Readers should be aware that *some* parts of this story are entirely fictitious, especially that speed-time graph! 😀

## 10 Comments

曜

日

Please correct me if i'm wrong:

Since both parties are moving at a constant rate, finding the LCM of the time taken for each lap would determine that, with LCM bounded between 2400 and 5400 (2400 being the 10 laps and 5400 being the time left)

Takahashi Brother's speed = 4*60=240s/lap

Ms Loi's speed = 165s/lap

Prime factorisation:

240=2

^{4}*3*5165=3*5*11

LCM=2

^{4}*3*5*11=2640Since the LCM is 2640, it is within the boundaries of 2400 and 5400. Therefore, Ms Loi would win! ^.^

PS: Ms Loi, would you change direction if you come to rest? 😛

曜

日

@Math Racer: Speaking through the walkie-talkie set ...

*radio static noise*

Roger

Math Racer! Miss Loi reads your solution loud and clear!However, using LCM will only yield the time when Miss Loi and the brothers next arrive together at their same original

starting positionsagain!*radio static noise*

But as Miss Loi is behind the brothers by 10 laps from the start, she'll need to physically overtake them many times - possibly at different points on the track (not necessary at the same starting point) before catching up and finally overtaking them

at the race distancein order to win the race!*radio static noise*

So the race may not be so easily won (if it is winnable in the first place)!!!

Over and out!!!

*radio static noise*

曜

日

@Miss Loi: I see, guess there is no way around it...

Since the average speeds of both rivals remain constant, the distance of 10 laps divided by the difference in speed must be lesser than 90min.

Takahashi Brother's speed = 4min/lap

Ms Loi's speed = 2.75min/lap (read from graph)

Difference = 4-2.75 = 1.25 min/lap

Thus, time taken for 10 laps = 10*1.25=12.5min

Since 12.5min < 90min, Ms Loi would win! ^.^ (I hope)

曜

日

@Math Racer: Speaking through the walkie-talkie set ...

*radio static noise*

This merely means that Miss Loi is able to complete 10 laps at 12.5 minutes faster than the Takahashi Brothers!

But with Miss Loi's

speedof 1/165 laps/second, she has only traveled adistance(note this is the 2^{nd}time this word is highlighted) of ... 1/165 × (12.5 × 60 seconds) = 4.545 laps within this 12.5 minutes.Hardly enough to make up for her 10-lap deficit at the start!

*radio static noise*

曜

日

Really it is an interesting stuff to hear at this moment. I am sporty person too and have to say too that because the average speeds of both rivals remain constant, the distance of 10 laps divided through the difference in speed has to be lesser than 90min.

曜

日

10 laps would take Racer Loi 27.5 minutes to complete

(since she's going at 2.75min/lap)

Every lap Racer Loi does lets her gain 1.25 minutes (4min-2.75min=1.25min)

So, Racer Loi needs 22 laps to catch up the lost laps.

22x2.75=60.5min

Which means, Racer Loi Catches up with the Takahashi Brothers at 1 hours and 30 seconds later; more than enough under the 90 minute limit

曜

日

@Lee Kian Boon: So, mis loi!! MY ANSWER CORRECT OR NOT??

曜

日

@Lee Kian Boon: 对不起我的 Leng Lui 表妹现在正忙着打电话不得空来看这个 blog!

但是她叫我跟你说你的算发不够力。因为在这 60.5 分钟里我的 Leng Lui 表妹虽然跑了22圈，但那两辆 STIs 也有跑了15圈。我的 Leng Lui 表妹总共才吃他们7圈吧了。

我看我的 Leng Lui 表妹这场是输定了！！！

Translated:Sorry my cousin is currently busy with her phone calls right now.

But she asks to me to pass this message saying that according to your calculation:

In 60.5 min, Miss Loi has traveled 22 laps, but the Takahashi Brothers have also traveled 60.5/4 ≈ 15 laps.

So Miss Loi has only traveled 22 − 15 = 7 laps more than them in this period, and we still haven't taken into account the 10-lap headstart the Takahashi Brothers had.

Oh Noes! Is Miss Loi going to lose?????!!!

P.S. As a clue, at the time

twhen Miss Loi overtakes (as inreallyovertake the in terms of the entire race distance) the cars, what distance has she traveled? What distance has the Takahashi brothers traveled? 😉曜

日

Sorry I didnt come back to try again, was busy dealing with Os...

In my 2nd comment, i mixed up the min/lap and lap/min. The latter should be used instead of the former. So, here we go... (for the last time I hope)

Racer Loi's speed: 1/2.75 = 4/11 laps/min

Takahashi Brothers' speed: 1/4 laps/min

Difference in speed: 4/11 - 1/4 = 5/44 laps/min

Since Racer Loi's speed is constantly faster, Racer Loi would definitely catch up. Whether or not it's in the 90-min limit is another question....

Time taken: 10laps / (5/44) laps/min = 88min

Thus, Racer Loi would meet the Brothers at the final 2mins. (praying hard that it's not wrong... D:)

曜

日

@Math Racer: *steps out of car*

*removes sweaty helmet*

Sorry that it has taken awhile for Miss Loi to come back.

Miss Loi took some time during the holiday period to produce a video of what happened during that fateful day, along with some

kinematicspointers.Hopefully this will bring some closure to this nerve-wrecking episode 😉