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OlympiadBench / 2334 / Three microphones A,B and C are placed on a line such that A is …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Three microphones

A, B

and

C

are placed on a line such that

A

is $1 \mathrm{~km}$ west of

B

and

C

is $2 \mathrm{~km}$ east of

B

. A large explosion occurs at a point

P

not on this line. Each of the three microphones receives the sound. The sound travels at $\frac{1}{3} \mathrm{~km} / \mathrm{s}$ . Microphone

B

receives the sound first, microphone

A

receives the sound

\frac{1}{2}

s later, and microphone

C

receives it $1 \mathrm{~s}$ after microphone

A

. Determine the distance from microphone

B

to the explosion at

P

Plain-text mathematical notation (without MathML)

Three microphones A,B and C are placed on a line such that A is $1 \mathrm{~km}$ west of B and C is $2 \mathrm{~km}$ east of B. A large explosion occurs at a point P not on this line. Each of the three microphones receives the sound. The sound travels at $\frac{1}{3} \mathrm{~km} / \mathrm{s}$. Microphone B receives the sound first, microphone A receives the sound (1)/(2) s later, and microphone C receives it $1 \mathrm{~s}$ after microphone A. Determine the distance from microphone B to the explosion at P.

Original LaTeX notation

Three microphones $A, B$ and $C$ are placed on a line such that $A$ is $1 \mathrm{~km}$ west of $B$ and $C$ is $2 \mathrm{~km}$ east of $B$. A large explosion occurs at a point $P$ not on this line. Each of the three microphones receives the sound. The sound travels at $\frac{1}{3} \mathrm{~km} / \mathrm{s}$. Microphone $B$ receives the sound first, microphone $A$ receives the sound $\frac{1}{2}$ s later, and microphone $C$ receives it $1 \mathrm{~s}$ after microphone $A$. Determine the distance from microphone $B$ to the explosion at $P$.

answer type

Numerical

is multiple answer

false

language

English

question type

Open-ended

subject

Math

unit

km

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Source and history

upstream_id / Original problem ID: 2334
task_id: c0103a9e-f4ab-52e2-bd48-4c381751e751
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2334
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

initial import