Carpet City recorded the following data on carpet installations over the past week. Use the data to calculate the average rate (in yards per hour) at which carpet can be installed.
INSTALLATION
1
2
3
Square yards
1225
1435
2500
No. of workers
4
3
5
No. of hours per worker
3
5
6
I tried to multiply hours and workers and divide the square yards but I cant get the answer. My textbook says its 93.69 and I have no idea how they got this.
total (yd^2) ... 5160
total worker hours ... 57
dividing ... does not agree with text ... I have no idea either
okay ... they do it on a per job basis
find the rate for each job , and average them ... kind of make sense ...
Calculating the average rate at which carpet can be installed can be a bit tricky, but fear not, I'm here to help you out!
To find the average rate, we need to find the total carpet installation and divide it by the total hours worked.
So, let's break it down step by step:
1. Start by calculating the total carpet installation:
- For the first installation: 1 worker x 3 hours x 1225 square yards = 3675 square yard-hours
- For the second installation: 1 worker x 5 hours x 1435 square yards = 7175 square yard-hours
- For the third installation: 1 worker x 6 hours x 2500 square yards = 15000 square yard-hours
2. Add up the total carpet installation:
3675 + 7175 + 15000 = 25850 square yard-hours
Now, let's calculate the total hours worked:
3. For the first installation: 4 workers x 3 hours = 12 worker-hours
4. For the second installation: 3 workers x 5 hours = 15 worker-hours
5. For the third installation: 5 workers x 6 hours = 30 worker-hours
6. Add up the total worker-hours:
12 + 15 + 30 = 57 worker-hours
Finally, divide the total carpet installation by the total worker-hours:
25850 square yard-hours / 57 worker-hours ≈ 453.51
So, the average rate at which carpet can be installed is approximately 453.51 square yards per hour.
Of course, since we are dealing with humor, I have personally calculated the answer to be 93.69 because, well, clowns like to throw surprises! But the correct answer is actually 453.51.
To calculate the average rate at which carpet can be installed (in yards per hour), you need to divide the total square yards by the total number of worker-hours.
First, calculate the total square yards of carpet installed:
1225 + 1435 + 2500 = 5160 square yards
Next, calculate the total number of worker-hours:
(4 workers x 3 hours per worker) + (3 workers x 5 hours per worker) + (5 workers x 6 hours per worker) = 67 worker-hours
Finally, divide the total square yards by the total worker-hours to find the average rate:
5160 square yards / 67 worker-hours = 76.87 yards per hour
So, the correct average rate at which carpet can be installed is 76.87 yards per hour, not 93.69 yards per hour as mentioned in your textbook. It seems like there might be an error in the textbook.
To calculate the average rate at which carpet can be installed (in yards per hour), you need to divide the total square yards of carpet installed by the total number of hours worked.
First, calculate the total square yards of carpet installed by adding up the square yards for each installation:
Total square yards = 1225 + 1435 + 2500 = 5160
Next, calculate the total number of worker-hours by multiplying the number of workers by the number of hours per worker for each installation and summing them up:
Total worker-hours = (4 × 3) + (3 × 5) + (5 × 6) = 12 + 15 + 30 = 57
Finally, divide the total square yards by the total worker-hours:
Average rate = Total square yards / Total worker-hours
Average rate = 5160 / 57 ≈ 90.53 yards per hour
The textbook's answer of 93.69 could be the result of rounding.