Question

Кот Матроскин и Шарик выпивают вместе бак молока за 56 минут. Шарик и Дядя Фёдор выпивают такой же бак молока за 72 минуты. Дядя Фёдор и Кот Матроскин выпивают такой же бак молока за 63 минуты. За сколько минут выпьют такой же бак молока Кот Матроскин, Шарик и Дядя Фёдор, если будут делать это одновременно?

Answer 1

Пусть m - время, которое нужно Матроскину, чтобы выпить все молоко самому, s - время, которое нужно Шарикуу, чтобы выпить все молоко самому, f - время, которое нужно дяде Федору, чтобы выпить все молоко самому. Все молоко - 1, тогда за 1 минуту матроскин выпьет $\frac{1}{m}$ часть молока, Шарик $\frac{1}{s}$ часть молока, а дядя Федор - $\frac{1}{f}$ часть молока. тогда:
$\left \{ {{ \frac{1}{m}+ \frac{1}{s}= \frac{1}{56} } \atop { \frac{1}{s} + \frac{1}{f} = \frac{1}{72} } } \atop { \frac{1}{f} + \frac{1}{m} = \frac{1}{63} } \right.$
Сложим эти три уравнения и получим: 
$2*( \frac{1}{m} + \frac{1}{s} + \frac{1}{f} )= \frac{1}{56} + \frac{1}{72} + \frac{1}{63} ; 2*( \frac{1}{m} + \frac{1}{s} + \frac{1}{f} )= \frac{9+8+7}{7*8*9};$

$2*( \frac{1}{m} + \frac{1}{s} + \frac{1}{f} )= \frac{24}{7*8*9}; \frac{1}{m} + \frac{1}{s} + \frac{1}{f}= \frac{1}{42}$
Если они все вместе за 1 минуту выпьют 1/42 часть всего молока, то все молоко всосут за 42 минуты

Answer 2

Problem Analysis

We are given information about the time it takes for different combinations of characters (Kot Matroskin, Sharik, and Dyadya Fyodor) to drink a certain amount of milk. We need to determine how long it will take for all three characters to drink the same amount of milk simultaneously.

Solution

Let's assign variables to represent the time it takes for each character to drink the milk: - Let K represent the time it takes for Kot Matroskin to drink the milk. - Let S represent the time it takes for Sharik to drink the milk. - Let D represent the time it takes for Dyadya Fyodor to drink the milk.

We are given the following information: - Kot Matroskin and Sharik drink a milk bucket together in 56 minutes. - Sharik and Dyadya Fyodor drink a milk bucket together in 72 minutes. - Dyadya Fyodor and Kot Matroskin drink a milk bucket together in 63 minutes.

To find the time it takes for all three characters to drink the same amount of milk simultaneously, we need to find the least common multiple (LCM) of K, S, and D.

Calculation

To find the LCM of three numbers, we can use the following formula: LCM(K, S, D) = LCM(LCM(K, S), D)

Using this formula, we can find the LCM of the given times.

Calculation Steps

1. Find the LCM of K and S: - LCM(K, S) = (K * S) / GCD(K, S) - We can find the GCD (Greatest Common Divisor) of K and S using the Euclidean algorithm. - Let's assume K = 56 and S = 72. - GCD(56, 72) = 8 - LCM(K, S) = (56 * 72) / 8 = 504

2. Find the LCM of LCM(K, S) and D: - LCM(LCM(K, S), D) = (LCM(K, S) * D) / GCD(LCM(K, S), D) - Let's assume D = 63. - GCD(504, 63) = 63 - LCM(LCM(K, S), D) = (504 * 63) / 63 = 504

Therefore, it will take 504 minutes for Kot Matroskin, Sharik, and Dyadya Fyodor to drink the same amount of milk simultaneously.

Answer

It will take 504 minutes for Kot Matroskin, Sharik, and Dyadya Fyodor to drink the same amount of milk simultaneously.

Note

Please note that the given problem is based on fictional characters from a popular Russian children's book series called "Kot Matroskin" by Eduard Uspensky. The problem does not have a real-world application and is purely for entertainment purposes.