Question 506927
Let 
length of end = x
length of beginning = 1/6 * x = x/6
length of middle = 1/2 * x = x/2

length of end + length of beginning + length of middle = Total length
x+(x/6)+(x/2)=170
Multiply by 6 both sides of the equation (6 is LCM of 6, 2)
6*(x+(x/6)+(x/2))=6*170
6x+x+(3*x)=1020
6x+x+3x=1020
10x=1020
Divide by 10 both sides of the equation
10x/10=1020/10
x=102
length of end = x = 102 Seconds
length of beginning = 102/6 = 17 Seconds
length of middle = x/2 = 102/2 = 51 Seconds
length of end + length of beginning + length of middle = Total length
102+17+51=170
170=170