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#### nycmathdad

##### Member

- Mar 21, 2021

- 75

- Thread starter nycmathdad
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- Thread starter
- Banned
- #1

- Mar 21, 2021

- 75

- Feb 21, 2015

- 85

Spider marriage is complicated. Sometimes, you just gotta mind your own biz.I ...

I love the question in your signature. It seems like a simple ratio problem. If we set up each ratio as "Proportion of Cask" : "Days"Beer soaked non sequitur ramblings follow.

Spider marriage is complicated. Sometimes, you just gotta mind your own biz.

Man

1 : 20

1/20 : 1

Woman

1 : x

1/x : 1

Together

1/20 + 1/x : 1

(x + 20)/(20x) : 1

1 : (20x)/(x + 20)

But the Together ratio is 1 : 14, so

$\displaystyle \begin{align*} \frac{20\,x}{x + 20} &= 14 \\

20\,x &= 14 \left( x + 20 \right) \\

20\,x &= 14\,x + 280 \\

6\,x &= 280 \\

x &= 46\,\frac{2}{3} \end{align*}$

So it will take the woman 46 hours and 40 minutes to finish the cask on her own.