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Here are some answers to the question below: Each color represent a different response.

Four singers take part in a musical round of 4 equal lines, each finishing after singing the line through three times.

The second singer begins when the first singer begins the second line, the third singer begins when the first singer begins the third line, the fourth singer begins when the first singer begins the fourth line. The fraction of the total singing time that all four are singing at the same time is:

A. 3/4
B. 3/5
C. 2/3
D. 5/6
E. 8/15

I found the total time as 7 lines. (4 lines for the first singer and then 3 lines after him for the last singer). The only time all the four all singing together is when the first singer sings the last line.

I’m a bit confused >.<” Do they all finish after singing 4 lines? What do you mean by, singing the line through 3 times? =S

I interpreted singing four lines three times as having a total of 12 lines that the singers continuously cycle through. Remember that and you should be able to find the answer using your previous method.

What i understood was that the singer sings 3 times a line and there are four lines in all. the first singer obviously starts first, after he finishes the first line (all the 3 times i suppose) he starts the second line, and just at that moment the second singer starts his/her first line. and so on…..

 You really should specify that the competition isn’t happening right now.  

I think you approaching it a tad wrong, because the question says all of them sing their lines 3 times AND when one finishes the other starts. The way I did it was to make a chart using the given algorithm and count the answer comes to be 9/15 or 3/5. However, there is an easier way of doing this. You know that the first singer will sing 4 lines 3 times, thus 12 times. But the last singer starts singing at the beginning of #1’s last line and therefore will end 3 lines after, making 15. so there are 3 + 3 times all four are not in unison. so (6-15)/15 = 9/15 or 3/5

L1 | 1 | 1,2,3,4 |1,2,3,4 |2,3,4

L2 | 1,2 | 1,2,3,4 |1,2,3,4 |3,4

L3 | 1,2,3 | 1,2,3,4 |1,2,3,4 |4

L4 | 1,2,3,4 | 1,2,3,4 |1,2,3,4

Any other answer? please leave it in the comment section of the blog!

Source : www.physicsforums.com