It looks like there are multiple distinct parts to your question which might be a bit mixed up. To provide a detailed, step-by-step solution, let's break it down into manageable parts and address each one clearly:
1. Find Total Earning from [tex]$p$[/tex] Vegetal Rin:
- Let's assume the total earnings from selling vegetal rin is represented by [tex]\( E \)[/tex].
2. How Much He Earns His Earning to Ruth the Family Every Night:
- Let's assume how much he allocates for his family every night is denoted as [tex]\( F \)[/tex].
3. If He Spends [tex]\(\frac{2}{5}\)[/tex] Pat in a Month, How Much Does He Save:
- To find out how much he saves, let's assume his total monthly earnings are denoted as [tex]\( M \)[/tex].
- He spends [tex]\(\frac{2}{5}\)[/tex] of [tex]\( M \)[/tex], so the amount spent is [tex]\(\frac{2}{5}M\)[/tex].
- The amount he saves is the remaining part of his monthly earnings: [tex]\( M - \frac{2}{5}M \)[/tex].
4. Different Sizes to Fill Water: One Pipe Can Fill [tex]\(\frac{1}{4}\)[/tex] Part in Thry:
- This part of the question is slightly unclear. However, we'll assume you are asking about how long it takes for multiple pipes to fill a tank if one pipe can fill [tex]\(\frac{1}{4}\)[/tex] of the tank in a certain amount of time.
Given the mixed-up nature of the question, let's handle the frequent elements mentioned, assuming [tex]\( p \)[/tex], [tex]\( E \)[/tex], [tex]\( F \)[/tex], and [tex]\( M \)[/tex] are related to "Pat" which seems to mean total income/earnings.
### Step-by-Step Breakdown:
1. Total Earning from [tex]\( p \)[/tex] Vegetal Rin:
- Let's redefine this earning as [tex]\( p \)[/tex].
- The total earnings from selling vegetal rin is represented by [tex]\( p \)[/tex].
2. Earnings for the Family Every Night:
- Assume overall monthly earnings are [tex]\( M \)[/tex] and a portion [tex]\( F \)[/tex] is assigned to family needs every night.
- If he earns [tex]\( F \)[/tex] every night for 30 nights, monthly:
[tex]\[
F = \frac{M}{30}
\][/tex]
3. Monthly Spending and Saving:
- Given he spends [tex]\(\frac{2}{5}\)[/tex] of his total earnings,
[tex]\[
\text{Spent amount} = \frac{2}{5}M
\][/tex]
- Savings would be the remaining [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[
\text{Savings per month} = M - \frac{2}{5}M = \frac{3}{5}M
\][/tex]
4. Filling Water with Pipes:
- If one pipe fills [tex]\(\frac{1}{4}\)[/tex] of the tank in a certain time, let's denote the time as [tex]\( T \)[/tex].
- In [tex]\( T \)[/tex] units of time, the tank is [tex]\(\frac{1}{4}\)[/tex] full.
- Suppose you have multiple pipes working simultaneously:
- Having 4 such pipes working together would fill the tank in the same [tex]\( T \)[/tex] units of time.
So, for final clarifications or extending your question logically:
- Please provide exact values for [tex]\( p \)[/tex], [tex]\( E \)[/tex], and [tex]\( F \)[/tex], [tex]\( M \)[/tex].
- Clarify how the pipes integrate into the scenario if you have specifics.
This should streamline your mixed-up question into clear, actionable insights. For best practices in mathematical analysis, always ensure clarity in variable assignment and scenario description.
