Question

Дежурные первого отряда за 6 минут чистят 24 картофелины, а дежурные второго отряда за 9 мин - 45 картофелин. За сколько минут совместной работы они почистят 198 картофелин?

Answer 1

1) 24 / 6 = 4 (картофелины / мин) чистит дежурный 1-го отряда

2) 45 / 9 = 5 (картофелины / мин) чистит дежурный 2-го отряда

3) 198 / (4 + 5) = 22 (минуты) почистиют картофель вместе два дежурных
Ответ: 22 минуты 

Answer 2

Calculating the Time Taken to Clean Potatoes

To calculate the time taken for the first and second teams to clean 198 potatoes, we can use the concept of "work done" and "time taken" to find the combined time taken by both teams.

Let's denote: - T1: Time taken by the first team to clean 24 potatoes - T2: Time taken by the second team to clean 45 potatoes - W1: Work done by the first team - W2: Work done by the second team - T: Combined time taken to clean 198 potatoes

We can use the formula: \[ \text{Work} = \text{Rate} \times \text{Time} \] \[ \text{Rate} = \frac{\text{Work}}{\text{Time}} \]

The rate of work for the first team is: \[ \text{Rate}_1 = \frac{24}{T1} \] The rate of work for the second team is: \[ \text{Rate}_2 = \frac{45}{T2} \]

The combined rate of work for both teams is: \[ \text{Combined Rate} = \text{Rate}_1 + \text{Rate}_2 \]

Using the combined rate, we can find the combined time taken to clean 198 potatoes: \[ \text{Combined Rate} = \frac{198}{T} \]

Calculating the Combined Time

To find the combined time taken to clean 198 potatoes, we can use the rates of work for the first and second teams.

The combined rate of work for both teams is: \[ \text{Combined Rate} = \frac{198}{T} = \text{Rate}_1 + \text{Rate}_2 \]

We can solve for T using the given values for T1 and T2.

Solution

Using the given information: - T1 = 6 minutes - T2 = 9 minutes

We can calculate the combined rate and then find the combined time taken to clean 198 potatoes.

\[ \text{Rate}_1 = \frac{24}{6} = 4 \text{ potatoes/minute} \] \[ \text{Rate}_2 = \frac{45}{9} = 5 \text{ potatoes/minute} \]

The combined rate is: \[ \text{Combined Rate} = 4 + 5 = 9 \text{ potatoes/minute} \]

Now, we can find the combined time taken to clean 198 potatoes: \[ \frac{198}{T} = 9 \] \[ T = \frac{198}{9} \] \[ T ≈ 22 \text{ minutes} \]

Therefore, the first and second teams working together will clean 198 potatoes in approximately 22 minutes.