Problem 20 · 2014 Math Kangaroo
Stretch
Arithmetic & Operations
division
An MP3 player has 5 songs: song A lasts 3 min, song B 2 min 30 s, song C 2 min, song D 1 min 30 s, and song E 4 min. The 5 songs play non-stop, one after another. Song C is playing when Andy leaves the house. Exactly one hour later he returns. Which song is playing when Andy comes back?
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Answer: A — A
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Hint 1 of 2
Add the five song lengths to get the length of one full loop, then see how many whole loops fit in an hour.
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Hint 2 of 2
After the whole loops, only a few minutes remain; track those extra minutes forward from where song C was playing.
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Approach: use the loop length, then carry the leftover minutes forward
- One loop A,B,C,D,E lasts 3 + 2.5 + 2 + 1.5 + 4 = 13 minutes.
- In 60 minutes there are 4 full loops (52 minutes) plus 8 extra minutes, so the playlist ends up 8 minutes further along the loop than when he left during song C.
- Starting from the beginning of C, 8 minutes later covers C, D, E (2 + 1.5 + 4 = 7.5 min) and reaches into song A.
- So song A is playing when Andy returns.
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