*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 *kinematics* pointers.

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

]]>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:)

]]>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 `t` when Miss Loi overtakes (as in *really* overtake the in terms of the entire race distance) the cars, what distance has she traveled? What distance has the Takahashi brothers traveled? 😉

So, mis loi!! MY ANSWER CORRECT OR NOT??

]]>(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

]]>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 *speed* of 1/165 laps/second, she has only traveled a **distance** (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*

]]>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)

]]>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 positions* again!

*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 distance** in 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*

]]>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*5

165=3*5*11

LCM=2^{4}*3*5*11=2640

Since 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? 😛

]]>