Question

Оформитель надувает за 2 ч 10 мин 78 шариков.Когда к нему присоеденился второй оформитель,то их производительность возрасла в 1 раз.А приготовить им надо было в 2 раза больше шариков.Хватит ли им 5 часов,чтобы выполнить всю работу

Answer 1

Нет им не хватит времени, что бы выполнить всю работу

Answer 2

Problem Analysis

We have two decorators who are inflating balloons. The first decorator can inflate 78 balloons in 2 hours and 10 minutes. When the second decorator joins, their productivity doubles, but they need to inflate twice as many balloons. We need to determine if they will be able to complete all the work in 5 hours.

Solution

To solve this problem, we need to calculate the total number of balloons that need to be inflated and compare it to the combined productivity of the two decorators.

Let's break down the problem step by step:

1. Calculate the productivity of the first decorator: - The first decorator can inflate 78 balloons in 2 hours and 10 minutes. - Convert 2 hours and 10 minutes to hours: 2 hours + 10 minutes / 60 minutes = 2.17 hours. - Calculate the productivity of the first decorator per hour: 78 balloons / 2.17 hours = 35.98 balloons per hour (rounded to 2 decimal places).

2. Calculate the total number of balloons that need to be inflated: - Since the second decorator's productivity doubles, the total number of balloons needed will be twice as much as the first decorator's productivity. - Total number of balloons needed = 2 * 78 balloons = 156 balloons.

3. Calculate the combined productivity of both decorators: - Since the second decorator's productivity doubles, their combined productivity will be the sum of the first decorator's productivity and the second decorator's doubled productivity. - Combined productivity = (35.98 balloons per hour) + (2 * 35.98 balloons per hour) = 107.94 balloons per hour (rounded to 2 decimal places).

4. Calculate the time required to inflate all the balloons: - Divide the total number of balloons needed by the combined productivity of both decorators to get the time required. - Time required = 156 balloons / 107.94 balloons per hour = 1.44 hours (rounded to 2 decimal places).

5. Compare the time required to inflate all the balloons with the given 5 hours: - If the time required is less than or equal to 5 hours, then the decorators will be able to complete all the work in 5 hours. - If the time required is greater than 5 hours, then the decorators will not be able to complete all the work in 5 hours.

Calculation

Based on the above analysis, let's calculate the time required to inflate all the balloons and check if it is less than or equal to 5 hours:

1. Productivity of the first decorator: 35.98 balloons per hour. 2. Total number of balloons needed: 156 balloons. 3. Combined productivity of both decorators: 107.94 balloons per hour. 4. Time required to inflate all the balloons: 1.44 hours.

Since the time required to inflate all the balloons is less than 5 hours, the decorators will be able to complete all the work in 5 hours.

Conclusion: Yes, the decorators will have enough time to complete all the work in 5 hours.