A-and-B-are-running-along-the-wall-of-a-square-park-The-corners-of-the-park-are-facing-north-south-east-and-west-and-are-named-N-S-E-W-respectively-They-start-at-E-and-run-towards-S-If-the-sp

Question Number 87034 by Zainal Arifin last updated on 02/Apr/20

A and B are running along the wall of

a square park . The corners of the park

are facing north, south, east and west

and are named N, S, E, W respectively .

They start at E and run towards S . If

the speed of A is 6 tines that of B, where

do they meet for the 27^{th} time ?

Answered by mr W last updated on 02/Apr/20

s a y s p e e d o f A i s v_{A} a n d s p e e d o f B

i s v_{B} . s a y p e r i m e t e r o f s q u a r e i s l .

s a y B h a s r u n a d i s t a n c e δ w h e n t h e y

m e e t f o r t h e f i r s t t i m e .

\frac{δ}{v_{B}} = \frac{l + δ}{v_{A}}

\frac{l + δ}{δ} = \frac{v_{A}}{v_{B}} = 6

\Rightarrow δ = \frac{l}{5}

w h e n t h e y m e e t f o r t h e s e c o n d t i m e

m e e t i n g p o i n t i s a t a d i s t a n c e \frac{2 l}{5}

f r o m s t a r t p o i n t E .

w h e n t h e y m e e t f o r t h e 5 t h t i m e

m e e t i n g p o i n t i s a t t h e s t a r t p o i n t .

w h e n t h e y m e e t f o r t h e 25 t h t i m e

m e e t i n g p o i n t i s a t t h e s t a r t p o i n t .

w h e n t h e y m e e t f o r t h e 27 t h t i m e

m e e t i n g p o i n t i s a t a d i s t a n c e \frac{2 l}{5}

f r o m s t a r t p o i n t E . i t i s b e t w e e n S

a n d W .

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