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 Four singers (Posted on 2018-03-26)
Four singers take part in a musical round of 4 equal lines, each fi nishing after singing the round through three times.
The second singer begins when the fi rst singer begins the second line,the third singer begins when the fi rst singer begins the third line,the fourth singer begins when the first singer begins the fourth line.

Find the fraction of the total singing time that all four are singing at the same time.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 Trick or Treat? (spoiler) | Comment 2 of 3 |
Charlie's first solution is correct if each singer sings the round only once.

However, the problem says that each sings it 3 times.  The first singer sings 12 lines, and there are 3 more lines after he stops, for a total of 15 lines.  6 of these lines (the first 3 and the last 3) do not involve all 3 singers, so the requested fraction is 9/15 = 3/5.

 Posted by Steve Herman on 2018-03-26 11:44:46

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