# 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.

• jonah

#### Country Boy

##### Well-known member
MHB Math Helper
I think I did this before, but since Prove It brings it up:
" 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.

• jonah

#### jonah

##### Member
Beer soaked ramblings follow.
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.
I think I did this before, but since Prove It brings it up:
" 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.
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.
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!)
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?
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".

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#### topsquark

##### Well-known member
MHB Math Helper
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.
Don't post your personal opinions in the Chat Room and you'll probably do just fine.

-Dan

#### skeeter

##### Well-known member
MHB Math Helper
Don't post your personal opinions in the Chat Room and you'll probably do just fine.

-Dan