Problema Solution
Alice and Bob are riding on a merry-go-round at a fairground. Alice sits on a horse on the inner ring which completes a revolution every 20 seconds. Bob sits on a horse on the outer ring which moves at a different speed and takes 28 seconds to complete a revolution. At a certain moment they are next to each other. After how many more seconds are they on opposite sides of the centre of the merry-go-round.
Answer provided by our tutors
let
t = second after they are on opposite sides of the center of the merry-go-round
Aline: in t second will make t/20 revolutions
Bob: after t seconds will make t/28 revolutions
since after t seconds they are on the opposite sides the difference between them is (2k+1)/2 revolutions, where k is non-negative integer that is:
|t/20 - t/28| = (2k+1)/2
t/70 = (2k+1)/2
t = 70 (2k+1)/2
t = 35 (2k+1)
this means that every odd multiple of 35 seconds they will be on the opposite sides of the center of merry-go-round:
after 1*35 = 35 second they are on the opposite sides of the center of merry-go-round
after 3*35 = 105 second they are on the opposite sides of the center of merry-go-round
after 5*35 = 175 second they are on the opposite sides of the center of merry-go-round
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after (2k + 1)*35 seconds they are on the opposite sides of the center of merry-go-round