The amount of time required to stack boxes varies directly with the number of boxes inversely with the number of people who are stacking them. If 2 people can stack 60 boxes in 10 minutes, how many minutes will be required for 6 people to stack 120 boxes?
Well, it seems like stacking boxes is quite an interesting activity! Let's break down the problem.
First, we need to find the constant of variation. Since the time required to stack boxes varies directly with the number of boxes and inversely with the number of people, we can set up the equation: time = k * (boxes/people).
Now, let's plug in the values given in the problem. When 2 people stack 60 boxes, we have 10 = k * (60/2). Simplifying this equation, we find that k = 1/3.
Using the constant of variation (k), we can solve for the time required when 6 people stack 120 boxes. This time will be given by: time = (1/3) * (120/6).
Calculating this, we find that the time required for 6 people to stack 120 boxes is 20 minutes.
So, to answer your question, it will take 6 people approximately 20 minutes to stack 120 boxes. I hope they bring their A-game and don't get too box-ed up in the process!
To solve this problem, we'll use the concept of direct and inverse variation.
Given that the time required to stack boxes varies directly with the number of boxes and inversely with the number of people, we can set up the following proportion:
Time taken (minutes) ∝ Number of boxes ÷ Number of people
Let's use the information given to solve for the constant of variation (k):
(10 minutes) ∝ (60 boxes) ÷ (2 people)
10 ∝ 30
k = 10/30
k = 1/3
Now we can use this value of k to answer the question:
Let x be the number of minutes required for 6 people to stack 120 boxes.
x ∝ 120 ÷ 6
x ∝ 20
So, we have x = 20.
Therefore, it will take 6 people 20 minutes to stack 120 boxes.
To solve this problem, we need to use the concepts of direct and inverse variation.
Let's break down the given information:
- The time required to stack boxes varies directly with the number of boxes. This means that as the number of boxes increases, the time required to stack them also increases.
- The time required to stack boxes varies inversely with the number of people. This means that as the number of people increases, the time required to stack the boxes decreases.
We are given that 2 people can stack 60 boxes in 10 minutes. We need to find out how many minutes it will take for 6 people to stack 120 boxes.
First, let's find the constant of variation for the number of boxes and time. We know that 2 people can stack 60 boxes in 10 minutes. So, the constant of variation (k) for the number of boxes and time is:
k = (number of boxes) / (time) = 60 / 10 = 6
Now, we can set up an equation using the constant of variation:
(number of people * number of boxes) / time = k
Plugging in the values we know:
(2 * 60) / 10 = 6
Next, we can use this equation to find the new time when 6 people are stacking 120 boxes:
(time when 6 people are stacking 120 boxes) = (number of people * number of boxes) / k
Plugging in the values:
(time when 6 people are stacking 120 boxes) = (6 * 120) / 6 = 720 / 6 = 120
Therefore, it will take 6 people 120 minutes to stack 120 boxes.
2 People: 60boxes/10min . = 6 boxes/min.
6 People: (6/2) * 6 = 18 boxes/min.
T = 120boxes * 1min/18boxes = 6.67 min.