Tons of Word Problems

Member
I have decided to use this forum mainly to increase my word problems skills. Of course, I will make use of this forum for mathematics in general but word problems set up will be my main focus. I hope to see your reply.

jonah

Member
Beer soaked non sequitur ramblings follow.
Spider marriage is complicated. Sometimes, you just gotta mind your own biz.

Prove It

Well-known member
MHB Math Helper
Beer soaked non sequitur ramblings follow.

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

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.