Question

Show work Plss oooooooo

Answer 1

`(3)/(8) \text{ hours.}`

Explanation:

Her first three videos totalled up to

`(7)/(8) + 1(1)/(4) + 2(1)/(2)\\=(7)/(8) + (5)/(4) + (5)/(2)\\=(7)/(8) + (5)/(4) \cdot (2)/(2) + (5)/(2) \cdot (4)/(4)\\=(7)/(8) + (10)/(8) + (20)/(8)\\=(7+10+20)/(8)\\=(37)/(8)`hours. To meet the
`5 = (40)/(8)` hour goal the shortest fouth video she can make is
`(40)/(8) - (37)/(8) = (3)/(8)` hours, because if the fourth video was any shorter, she'd end up with less than
`(37)/(8) + (3)/(8) = (40)/(8) = 5` hours in total (this is called a proof by contradiction). We are now done.

Answer 2

22.5 mins

Explanation:

To find what that video's length must be, subtract the previous videos' lengths from the requirement, 5 hours. (x is the video length of her fourth video)

7/8 + 1 1/4 + 2 1/2 + x = 5

To make adding these fractions easier, find a common denominator.

7/8 + 1 2/8 + 2 4/8 + x = 5

4 5/8 + x = 5

x = 3/8, or 22.5 minutes.