Question

A 190-second song is divided into 3 parts, the beginning, the middle, and the end. The beginning is 1/6 as long as the end. The middle part is 1/2 as long as the end. Find the length of each part.

The beginning is ____ seconds
The middle is _____ seconds
The end is ______ seconds

Answer 1

b is 19 seconds

m is 57 seconds

e is 114 seconds

Explanation:

total = b + m + e

total = 1/6e + 1/2e + e

190 = 1/6e + 1/2e + e

190 = 10/6e

190 * 3/5 = e

114 = e

(1/6)e = b = (1/6)(114) = 19

(1/2)e = m = (1/2)(114) = 57

Answer 2

The beginning part is 19 seconds.

The middle part is 57 seconds.

The end part is 114 seconds.

Explanation:

First, you have to form expressions. Let the end part be x :

Beginning = (1/6)x

Middle = (1/2)x

End = x

Next, you have to add up altogether equals to 190 :

(1/6)x + (1/2)x + x = 190

(5/3)x = 190

x = 190 ÷ (5/3)

x = 114 s

Lastly, you have to substitute the x-value into the expressions :

Beginning = (1/6)(114) = 19 s

Middle = (1/2)(114) = 57 s

End = 114 s