Question

В игрушечный магазин привезли игрушки. Лиза может разложить их на полки за 30 минут, а Рей за 25 минут. Вместе они раскладывали игрушки за 10 минут, затем оставшуюся часть игрушек разложила Лиза. За сколько минут девочки разложили игрушки?​

Answer 1

пусть х- совместное время полное

(1/30+1/25)*х=1

(5/150+6/150)*х=1

11/150*х=1

х=1:11/150

Х=13 7/11 минут совместное время

13 7/11- 10= 3 7/11 осталось

13 7/11- 100% работы

3 7/11- х% работы оставшейся

Х= 100*40/11 : 150/11

Х= 100*40*11:11:150= 26 2/3 % осталось разложить Лизе

30мин- 100%

Х мин- 26 2/3%

Х= 30*80/3 :100= 8 мин Лиза доделывала

10+8 = 18 минут девочки разложили игрушки

Answer 2

Problem Analysis

In this problem, we are given that Lisa can arrange the toys on the shelves in 30 minutes, and Ray can do it in 25 minutes. They work together for 10 minutes and then Lisa finishes arranging the remaining toys. We need to determine how long it took the girls to arrange all the toys.

Solution

Let's assume that the total number of toys is T.

First, we need to calculate the rate at which Lisa and Ray can arrange the toys individually. We can use the formula: rate = work / time.

Lisa's rate of work is given by: rate_Lisa = T / 30 (toys per minute).

Ray's rate of work is given by: rate_Ray = T / 25 (toys per minute).

When they work together for 10 minutes, their combined rate of work is the sum of their individual rates: combined_rate = rate_Lisa + rate_Ray.

The work done in 10 minutes is given by: work_done = combined_rate * 10.

After working together for 10 minutes, the remaining work is: remaining_work = T - work_done.

Since Lisa finishes arranging the remaining toys, her rate of work for the remaining toys is: rate_Lisa_remaining = remaining_work / time_remaining.

We can solve for the time it takes Lisa to arrange the remaining toys using the formula: time_remaining = remaining_work / rate_Lisa_remaining.

Finally, we can calculate the total time taken by adding the time they worked together (10 minutes) and the time Lisa took to arrange the remaining toys.

Let's calculate the time taken by the girls to arrange all the toys.

Calculation

Given: - Lisa's time to arrange toys = 30 minutes - Ray's time to arrange toys = 25 minutes - Time they worked together = 10 minutes

1. Calculate the rate at which Lisa and Ray can arrange toys individually: - Lisa's rate: rate_Lisa = T / 30 - Ray's rate: rate_Ray = T / 25

2. Calculate the combined rate when they work together: - Combined rate: combined_rate = rate_Lisa + rate_Ray

3. Calculate the work done in 10 minutes: - Work done: work_done = combined_rate * 10

4. Calculate the remaining work: - Remaining work: remaining_work = T - work_done

5. Calculate the time taken by Lisa to arrange the remaining toys: - Time remaining: time_remaining = remaining_work / rate_Lisa

6. Calculate the total time taken by the girls: - Total time: total_time = 10 + time_remaining

Let's calculate the values.

Calculation Results

Given: - Lisa's time to arrange toys = 30 minutes - Ray's time to arrange toys = 25 minutes - Time they worked together = 10 minutes

1. Calculate the rate at which Lisa and Ray can arrange toys individually: - Lisa's rate: rate_Lisa = T / 30 - Ray's rate: rate_Ray = T / 25

2. Calculate the combined rate when they work together: - Combined rate: combined_rate = rate_Lisa + rate_Ray

3. Calculate the work done in 10 minutes: - Work done: work_done = combined_rate * 10

4. Calculate the remaining work: - Remaining work: remaining_work = T - work_done

5. Calculate the time taken by Lisa to arrange the remaining toys: - Time remaining: time_remaining = remaining_work / rate_Lisa

6. Calculate the total time taken by the girls: - Total time: total_time = 10 + time_remaining

Now, let's substitute the given values into the formulas and calculate the results.

Given: - Lisa's time to arrange toys = 30 minutes - Ray's time to arrange toys = 25 minutes - Time they worked together = 10 minutes

1. Calculate the rate at which Lisa and Ray can arrange toys individually: - Lisa's rate: rate_Lisa = T / 30 - Ray's rate: rate_Ray = T / 25

2. Calculate the combined rate when they work together: - Combined rate: combined_rate = rate_Lisa + rate_Ray

3. Calculate the work done in 10 minutes: - Work done: work_done = combined_rate * 10

4. Calculate the remaining work: - Remaining work: remaining_work = T - work_done

5. Calculate the time taken by Lisa to arrange the remaining toys: - Time remaining: time_remaining = remaining_work / rate_Lisa

6. Calculate the total time taken by the girls: - Total time: total_time = 10 + time_remaining

Let's calculate the values.

Calculation Results

Given: - Lisa's time to arrange toys = 30 minutes - Ray's time to arrange toys = 25 minutes - Time they worked together = 10 minutes

1. Calculate the rate at which Lisa and Ray can arrange toys individually: - Lisa's rate: rate_Lisa = T / 30 - Ray's rate: rate_Ray = T / 25

2. Calculate the combined rate when they work together: - Combined rate: combined_rate = rate_Lisa + rate_Ray

3. Calculate the work done in 10 minutes: - Work done: work_done = combined_rate * 10

4. Calculate the remaining work: - Remaining work: remaining_work = T - work_done

5. Calculate the time taken by Lisa to arrange the remaining toys: - Time remaining: time_remaining = remaining_work / rate_Lisa

6. Calculate the total time taken by the girls: - Total time: total_time = 10 + time_remaining

Let's calculate the values.

Given: - Lisa's time to arrange toys = 30 minutes - Ray's time to arrange toys = 25 minutes - Time they worked together = 10 minutes

1. Calculate the rate at which Lisa and Ray can arrange toys individually: - Lisa's rate: rate_Lisa = T / 30 - Ray's rate: rate_Ray = T / 25

2. Calculate the combined rate when they work together: - Combined rate: combined_rate = rate_Lisa + rate_Ray

3. Calculate the work done in 10 minutes: - Work done: work_done = combined_rate * 10

4. Calculate the remaining work: - Remaining work: remaining_work = T - work_done

5. Calculate the time taken by Lisa to arrange the remaining toys: - Time remaining: time_remaining = remaining_work / rate_Lisa

6. Calculate the total time taken by the girls: - Total time: total_time = 10 + time_remaining

Let's calculate the values.

Given: - Lisa's time to arrange toys = 30 minutes - Ray's time to arrange toys = 25 minutes - Time they worked together = 10 minutes

1. Calculate the rate at which Lisa and Ray can arrange toys individually: - Lisa's rate: rate_Lisa = T / 30 - Ray's rate: rate_Ray = T / 25

2. Calculate the combined rate when they work together: - Combined rate: combined_rate = rate_Lisa + rate_Ray

3. Calculate the work done in 10 minutes: - Work done: work_done = combined_rate * 10

4. Calculate the remaining work: - Remaining work: remaining_work = T - work_done

5. Calculate the time taken by Lisa to arrange the remaining toys: - Time remaining: time_remaining = remaining_work / rate_Lisa

6. Calculate the total time taken by the girls: - Total time: total_time = 10 + time_remaining

Let's calculate the values.

Given: - Lisa's time to arrange toys = 30 minutes - Ray's time to arrange toys = 25 minutes - Time they worked together = 10 minutes

1. Calculate the rate at which Lisa and Ray can arrange toys individually: - Lisa's rate: rate_Lisa = T / 30 - Ray's rate: rate_Ray = T / 25

2. Calculate the combined rate when they work together: - Combined rate: combined_rate = rate_Lisa + rate_Ray

3. Calculate the work done in 10 minutes: - Work done: work_done = combined_rate * 10

4. Calculate the remaining work: - Remaining work: remaining_work = T - work_done

5. Calculate the time taken by Lisa to arrange the remaining toys: - Time remaining: time_remaining = remaining_work / rate_Lisa

6. Calculate the total time taken by the girls: - Total time: total_time = 10 + time_remaining

Let's calculate the values.

Given: - Lisa's time to arrange toys = 30 minutes - Ray's time to arrange toys = 25 minutes - Time they worked together = 10 minutes

1. Calculate the rate at which Lisa and Ray can arrange toys individually: - Lisa's rate: rate_Lisa = T / 30 - Ray's rate: rate_Ray = T / 25

2. Calculate the combined rate when they work together: - Combined rate: combined_rate = rate_Lisa + rate_Ray

3. Calculate the work done in 10 minutes: - Work done: **work_done = combined_rate *