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Bunuel

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01 Jun 2023, 01:28

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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

vedha0

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23 Jun 2023, 05:40

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good intuitive problem!

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12 Aug 2023, 08:44

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I think this is a high-quality question and I agree with explanation.

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24 May 2024, 14:58

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I think this is a high-quality question and I agree with explanation.

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30 Jun 2024, 08:15

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Starting Point: Buster starts walking from the trailer towards the studio at noon (12:00 PM).
Head Start: 20 minutes later, at 12:20 PM, Charlie starts walking from the studio towards the trailer. So, Buster has a 20-minute head start.
Speed: We know Buster walks at B miles per hour, and Charlie walks faster at C miles per hour .

---

Statement (1):

Charlie takes 55 minutes to reach the trailer from the studio. This doesn't tell us anything about where Buster is when they meet.

=> No sufficient

Statement (2):

Buster reaches the studio at the exact same time Charlie reaches the trailer.

=> Since Charlie started later but reaches the trailer at the same time as Buster reaches the studio (a shorter distance), it means Charlie must be much faster (C > B).

After C and B meets, each continues their journey and reach their respective destinations at the same time.

However, C is fater than B
=> For the period from their meeting each other until reaching their respective destination, the distance covered by C (m) is more than that covered by B (n)
=> Which mean B was closer to his destination (trailer) than to his startpoint (studio)

[___________m_____________][_______n________]
x---------------------------------------x------------------------x
Studio Point where B & C meet Trailer

=> Sufficient

Lo110l

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07 Jan 2025, 01:40

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Bunuel

Buster leaves the trailer at noon and walks towards the studio at a constant rate of B miles per hour. 20 minutes later, Charlie leaves the same studio and walks towards the same trailer at a constant rate of C miles per hour along the same route as Buster. Will Buster be closer to the trailer than to the studio when he passes Charlie?

(1) Charlie gets to the trailer in 55 minutes.

(2) Buster gets to the studio at the same time as Charlie gets to the trailer.

(1) is insufficient because we dont have any info for Buster from this

(2)
Let trailer and studio be "D" distance away.

Buster and Charlie will meet after (D-B/3)/(B+C) time.

Buster's distance from trailer when he meets Charlie = B/3 + B*((D-B/3)/(B+C)) = B/3(1-B/(B+C)) + BD/(B+C) = BC/3(B+C) + BD/(B+C)

Buster gets to studio after ( D-B/3 )/B
Charlie gets to studio after D/C
According to (2) both of them are equal

(D-B/3)/B = D/C <=> D = BC/3( C-B )

substitute the value of D, we get Buster's distance from trailer when he meets Charlie = (B/(B+C))( C/3 + BC/(3(C-B)) ) = (BC/(3(B+C)))( C/(C-B) )
= D*(C/(B+C)) > D/2 as we know that C>B as Charlier covers D in the same time as Buster covers D-B/3.

C>B <=> 2C > B+C <=> C/(B+C) > 1/2

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20 May 2025, 08:32

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I like the solution - it’s helpful.

Soham94

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26 May 2025, 22:38

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I like the solution - it’s helpful.

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20 Jul 2025, 06:59

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I like the solution - it’s helpful.

executor09

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15 Aug 2025, 06:07

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I like the solution - it’s helpful.

estvoluptas

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15 Aug 2025, 07:23

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I like the solution - it’s helpful.

isteducimus

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17 Sep 2025, 03:43

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In Statement 2, as they reach at same time, it means they have not passed each other during the way, else Charlie would have reached earlier as he is faster. So, Buster will be exactly at the studio when they both meet. Isn't it?
Also, Q says "Will Buster be closer to the trailer than to the studio when he passes Charlie?" - how would Buster pass Charlie when Charlie started later? It should be "...when Charlie passes Buster".
Is my understanding correct?

Bunuel

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17 Sep 2025, 03:55

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isteducimus

Unfortunately, nothing in your interpretation makes sense. They definitely pass each other; they had to meet, since they were walking directly toward each other on the same path.

The wording is fine: “when Buster passes Charlie” just means “when they pass each other.”

You should re-read the question, the solution, and the discussion carefully for proper context.