Question

Кот Том съедает жареную индейку за 20 мин , а мышонок Джерри -за 30 мин. .За сколько минут Том и Джерри съедят индейку вместе ?Помогите пожалуйста решить

Answer 1

$1) \frac{1}{20}+ \frac{1}{30} = \frac{2+3}{60}= \frac{1}{12}$ совместная скорость поедания индейки Томом и Джерри

$2) 1:\frac{1}{12}=12$ минут потребуется Тому и Джерри, чтобы съесть индейку.

Ответ 12 минут

Answer 2

Problem Analysis

We are given that Tom can eat a roasted turkey in 20 minutes, while Jerry can eat the same turkey in 30 minutes. We need to determine how long it will take for Tom and Jerry to eat the turkey together.

Solution

To solve this problem, we can use the concept of rates. The rate at which Tom eats the turkey is 1 turkey per 20 minutes, and the rate at which Jerry eats the turkey is 1 turkey per 30 minutes.

Let's assume that it takes x minutes for Tom and Jerry to eat the turkey together. In x minutes, Tom's rate of eating is (1 turkey / 20 minutes) and Jerry's rate of eating is (1 turkey / 30 minutes).

According to the principle of addition, the combined rate of Tom and Jerry eating the turkey together is the sum of their individual rates. Therefore, the combined rate is:

(1 turkey / 20 minutes) + (1 turkey / 30 minutes)

To find the time it takes for Tom and Jerry to eat the turkey together, we can set up the equation:

(1 turkey / 20 minutes) + (1 turkey / 30 minutes) = 1 turkey / x minutes

Now, we can solve this equation to find the value of x, which represents the time it takes for Tom and Jerry to eat the turkey together.

Calculation

Let's solve the equation:

(1 turkey / 20 minutes) + (1 turkey / 30 minutes) = 1 turkey / x minutes

To simplify the equation, we can find the least common multiple (LCM) of 20 and 30, which is 60. Multiplying both sides of the equation by 60x, we get:

3x + 2x = 60

Combining like terms, we have:

5x = 60

Dividing both sides by 5, we find:

x = 12

Therefore, it will take Tom and Jerry 12 minutes to eat the turkey together.

Answer

Tom and Jerry will eat the roasted turkey together in 12 minutes.