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# Buster leaves the trailer at noon and walks towards the studio at a co

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Manager
Joined: 12 Mar 2014
Posts: 62
GPA: 3.4
Buster leaves the trailer at noon and walks towards the studio at a co  [#permalink]

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02 Oct 2014, 11:39
16
00:00

Difficulty:

65% (hard)

Question Stats:

57% (02:13) correct 43% (02:49) wrong based on 344 sessions

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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.

Request: This question can be solved by explaining in words, however, could someone solve it by algebra please? I got stuck when I tried to do it myself

THanks!

Gordonf35

M06-19
Math Expert
Joined: 02 Sep 2009
Posts: 52902
Re: Buster leaves the trailer at noon and walks towards the studio at a co  [#permalink]

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03 Oct 2014, 00:02
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3
gordonf35 wrote:
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.

Request: This question can be solved by explaining in words, however, could someone solve it by algebra please? I got stuck when I tried to do it myself

THanks!

Gordonf35

M06-19

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. No info about Buster. Not sufficient.

(2) Buster gets to the studio at the same time as Charlie gets to the trailer --> Charlie needed 20 minutes less than Buster to cover the same distance, which means that the rate of Charlie is higher than that of Buster. Since after they pass each other they need the same time to get to their respective destinations (they get at the same time to their respective destinations) then Buster had less distance to cover ahead (at lower rate) than he had already covered (which would be covered by Charlie at higher rate). Sufficient.

This question is discussed here: devil-s-dozen-129312.html You can check alternate solutions in that topic.
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Joined: 23 Jan 2018
Posts: 25
Location: United States
Concentration: Marketing, Nonprofit
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Re: Buster leaves the trailer at noon and walks towards the studio at a co  [#permalink]

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17 Mar 2018, 17:07
it seems that the solution of bb is the only best solution for this question. To visualize the solution, ones just need to draw the distance and the point where the two pass each other.
Manager
Joined: 22 May 2017
Posts: 120
Buster leaves the trailer at noon and walks towards the studio at a co  [#permalink]

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24 Jan 2019, 03:14
skidstorm wrote:
it seems that the solution of bb is the only best solution for this question. To visualize the solution, ones just need to draw the distance and the point where the two pass each other.

I agree Bunuel's solution is precise one.
But whenever I stumble upon this question again , i forget the approach how to solve this and it takes me lot of time to figure out .
Especially when trying to solve it algebraically

So here is my visual solution . Hope it helps.

Given: C starts 20 min late than B
To find the relative position

3 possible meeting point i.e X
1. B -------X-------------------------------C

2. B ------------------X--------------------C

3. B -------------------------------X-------C

Stmnt 1 : Total C time 55 min .
With this info cannot find the meeting point whether 1,2 or 3

Stmnt 2 : Both reach at the same time to respective destinations (total distance is same)

Since we know C starts late still covers same distance .
Hence C is speeder is greater than B

Now lets check if stmnt 2 satisfies any of the meeting point

[When they meet they have same time to cover remaining respective distances]

1.) B -------X-------------------------------C

B has to cover larger distance XC and
C has to cover shorter distance XB

But C is faster than B hence it can cover smaller distance before B could cover large distance
hence this meeting point is wrong

2.) B -----------------X--------------------C
Same remaining distance with same time
but since speed is not same
this scenario is also not possible

3.) B --------------------------X-----------C

B has to cover smaller distance XC and
C has to cover Larger distance XB

C can achieve this it as its speed is more B .
So it can reach , till B slowly reaches the studio . This is the only possibility for relative position.
i.e closer B is closer to studio

B
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Buster leaves the trailer at noon and walks towards the studio at a co   [#permalink] 24 Jan 2019, 03:14
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