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#### nycmathdad

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- Mar 21, 2021

- 75

- Thread starter nycmathdad
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- Feb 21, 2015

- 94

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.

- Jan 30, 2018

- 734

" If one priest can pray a soul out of purgatory in 5 hours, while it takes a second priest 8 hours, how long will it take if the two priests pray together?"

So one priest prays at the rate of "one soul per 5 hours"" or "1/5 soul per hour" and the other at the rate of "one soul per eight hours" or "1/8 soul per hour". When they pray together, their rates add (I think that's stated in the bible) so 1/5+ 1/8= 8/40+ 5/40= 13/40". So it will require 40/13= 3 and 1/40 hour= 3 hours and 1.5 minutes.

- Feb 21, 2015

- 94

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.

It amazes me that people who took the time to solve my two preposterous signature questions were able to control their laughter after seeing them for the first time.

" If one priest can pray a soul out of purgatory in 5 hours, while it takes a second priest 8 hours, how long will it take if the two priests pray together?"

So one priest prays at the rate of "one soul per 5 hours"" or "1/5 soul per hour" and the other at the rate of "one soul per eight hours" or "1/8 soul per hour". When they pray together, their rates add (I think that's stated in the bible) so 1/5+ 1/8= 8/40+ 5/40= 13/40". So it will require 40/13= 3 and 1/40 hour= 3 hours and 1.5 minutes.

Timios and Skipjack have also took a shot at them at

A man can drink a cask of wine in 20 days, but if his wife drinks with him it will take only 14 days — how long would it take for the wife alone?

Would it take the wife 41.67 days?

Soroban at

Hello, jonah1!

The man drinks the cask in 20 days.

In one day, he can drink $\frac{1}{20}$ of the cask.

. . In 14 days, he can drink $\frac{14}{20} \,=\,\frac{7}{10}$ of the cask.

The woman drinks the cask in $x$ days (alone).

In one day, she can drink $\frac{1}{x}$ of the cask.

. . In 14 days, she can drink $\frac{14}{x}$ of the cask.

Together, in 14 days, they can drink $\frac{7}{10} + \frac{14}{x}$ of the cask.

But we are told: together, in 14 days, they will drink the cask (one cask).

There is our equation! . . . $\frac{7}{10} + \frac{14}{x} \;=\;1$

Go for it!

Frick at

I have looked at these for so long, I just can't stand it any more:

When two people, or machines, etc. do something together, their rates add. Let the number of days the wife would take to drink a caskof wine be "x". Then her rate is $\frac{1}{x}$ "days per cask. Her husband's rate is $\frac{1}{20}$ and their rate together is $\frac{1}{14}$. We have $\frac{1}{x}+ \frac{1}{20}= \frac{1}{14}$. Multiply by the least common multiple of the denominators, 140x.

$140+7x=10x$

$140=3x$

$x=\frac{140}{3}$.

It would take the wife, alone, 46 and 2/3 days to drink the cask of wine.(I shall start experimenting to see how long it will take me to drink a cask of wine!)

This is even simpler, almost an arithmetic problem. The first priest prays at the rate $\frac{1}{5}$ "soul per hour" and the second priest prays at the rate of $\frac{1}{8}$ "soul per hour". Together they pray at the rate of $\frac{1}{5}+ \frac{1}{8}=\frac{8}{40}+ \frac{5}{40}= \frac{13}{40}$ "soul per hour". Together it would take $\frac{40}{13}$ or 3 and 1/13 "hour per soul".If one priest can pray a soul out of purgatory in 5 hours, while it takes a second priest 8 hours, how long will it take if the two priests pray together?

Last edited:

- Aug 30, 2012

- 1,183

Don't post your personal opinions in the Chat Room and you'll probably do just fine.

-Dan

- Mar 1, 2012

- 871

he’s already been banned …Don't post your personal opinions in the Chat Room and you'll probably do just fine.

-Dan

- Aug 30, 2012

- 1,183