Answer:
Step-by-step explanation:
The main part of the song is the end. The beginning length is based on the end and so is the middle length. The beginning length is 1/6 as long as the end, so if the end is our main unknown, x, the beginning is 1/6x. The middle is one-half as long as the end, so if the end is our main unknown, x, the middle is 1/2x. The sum of the 3 parts is 370, so:
[tex]x+\frac{1}{6}x+\frac{1}{2}x=370[/tex]
The GCF of those denominators is 6, so multiply through every term by 6 to get rid of the fractions:
[tex](6)x+(6)\frac{1}{6}x+(6)\frac{1}{2}x=(6)370[/tex]
Simplifying gives us
6x + x + 3x = 2220 and
10x = 2220 so
x = 222
That means that the end is 222 seconds, the bginning is 37 seconds, and the middle is 111 seconds.
