Question

Валя и Галя пропалывают грядку за 8 минут ,а одна Галя -за 10 минут.За ско-ко минут пропалывает грядку одна Валя?Помогите ,пожалуйстаааа

Answer 1

Problem Analysis

We are given that Valya and Galya can weed a garden bed in 8 minutes together, while Galya can do it alone in 10 minutes. We need to determine how long it would take Valya to weed the garden bed alone.

Solution

Let's assume that Valya's rate of weeding is V beds per minute and Galya's rate is G beds per minute. We can set up the following equations based on the given information:

1. Valya and Galya can weed a garden bed in 8 minutes together: - In 1 minute, Valya completes 1/V of the garden bed. - In 1 minute, Galya completes 1/G of the garden bed. - Together, they complete 1/8 of the garden bed in 1 minute. - So, the equation is: 1/V + 1/G = 1/8. 2. Galya can weed a garden bed alone in 10 minutes: - In 1 minute, Galya completes 1/G of the garden bed. - So, the equation is: 1/G = 1/10. To find the time it takes Valya to weed the garden bed alone, we need to solve these equations.

Calculation

Let's solve the equations to find the values of V and G:

From equation we have: 1/G = 1/10. Simplifying, we get: G = 10.

Substituting G = 10 in equation we have: 1/V + 1/10 = 1/8. Simplifying, we get: 1/V = 1/8 - 1/10.

Finding the common denominator and simplifying, we get: 1/V = 5/40 - 4/40 = 1/40. So, V = 40.

Answer

Therefore, Valya can weed the garden bed alone in 40 minutes.

Please let me know if I can help you with anything else.