Question

Маша чистит картошку за 20 минут, Даша это же количество картошки- за 30 минут, а Надя это же количество картошки - за 60 минут. За какое время они почистят это количество картошки втроём.

Answer 1

За 60 минут.............................

Answer 2

Calculation of Time Taken to Peel Potatoes

To determine the time it will take for Masha, Dasha, and Nadya to peel the same amount of potatoes together, we need to consider their individual rates of peeling potatoes.

According to the information provided: - Masha can peel the potatoes in 20 minutes. - Dasha can peel the same amount of potatoes in 30 minutes. - Nadya can peel the same amount of potatoes in 60 minutes.

To find the combined time it will take for all three of them to peel the potatoes, we can calculate the harmonic mean of their individual rates.

The harmonic mean is calculated as follows: Harmonic Mean = Total Work / (1st Rate + 2nd Rate + 3rd Rate)

Let's calculate the time it will take for them to peel the potatoes together:

1. Calculate the individual rates: - Masha's rate = 1/20 potatoes per minute - Dasha's rate = 1/30 potatoes per minute - Nadya's rate = 1/60 potatoes per minute

2. Calculate the harmonic mean: - Harmonic Mean = 3 / ((1/20) + (1/30) + (1/60))

Using this formula, we can calculate the time it will take for them to peel the potatoes together.

Calculation:

The harmonic mean of the rates is approximately 0.024 potatoes per minute.

To calculate the time it will take for them to peel the same amount of potatoes together, we can use the formula:

Time = Amount of Potatoes / Combined Rate

Since the amount of potatoes is not specified in the question, we cannot provide an exact answer. However, we can use a hypothetical amount of potatoes to demonstrate the calculation.

Let's assume they need to peel 60 potatoes.

Using the combined rate of 0.024 potatoes per minute, we can calculate the time it will take for them to peel 60 potatoes:

Time = 60 potatoes / 0.024 potatoes per minute

Calculating this, we find that it will take them approximately 2500 minutes to peel 60 potatoes together.

Please note that the actual time will vary depending on the amount of potatoes they need to peel.

Conclusion:

In conclusion, the time it will take for Masha, Dasha, and Nadya to peel the same amount of potatoes together depends on the amount of potatoes they need to peel. By calculating the harmonic mean of their individual rates, we can determine their combined rate. Using this combined rate, we can calculate the time it will take for them to peel a specific amount of potatoes.