We are doing a small group project and my group members and I are very confused. The project description:
Using the variables provided below, you are working with your group to make a recommendation to the township directors. Currently we mow the grass surounding the highway. A proposal was made by a landscaping company to cover the area with a wild flower that will not require mowing, but trimming periodically. It is your team's job to determine if we should plant the groundcover or if we should just continue to mow the grass by the highway.
Variables given:
Road length in miles - 5
Roadside Distance in yards (aka the width) - 20
Number of exits - 4
Exit size in yards - 50
Labor Cost per hour - $15
Cost of gas - $2.65
Mowing frequency on average - Every 10 days for nine months
Deck size of the mower - 30 inches
My group has already figured out the wild flower data, so I didn't include those variables. What we are struggling to figure out is how many hours it takes to mow, so that we can figure out how much money will be given as the labor cost ($15 x ___ hours). We have figured out that the area that is mowed, when the exits are taken away since they don't need to be mowed, is 172,000 square yards, and the teacher has confirmed that this is correct.
What we don't get is how to possibly figure out the time/hours it takes when all we are given are yards and measurements. The teacher mentioned something about calculating the "passes," or number of times the mower goes up and down the rows, but we don't get how that could help us find the time. Is it even possible? Your help is appreciated, especially since this is a graded project. Thank you so much!
To calculate the time it takes to mow the grass, you can start by determining the area that can be covered by the mower in one pass. This will help you estimate the number of passes required to complete the mowing.
Here's how you can approach the calculation:
1. Calculate the area covered by the mower in one pass:
- Convert the deck size of the mower from inches to yards. Since 1 yard equals 36 inches, the deck size of 30 inches is equivalent to 30/36 = 0.8333 yards.
- Multiply the deck size (in yards) by the roadside distance (in yards) to get the area covered by the mower in one pass. In this case, it would be 0.8333 yards * 20 yards = 16.67 square yards.
2. Determine the total area to be mowed:
- Subtract the area covered by the exits from the total area. In this case, the total area is given as 172,000 square yards.
3. Calculate the number of passes required:
- Divide the total area to be mowed by the area covered by the mower in one pass. In this case, it would be 172,000 square yards / 16.67 square yards = approximately 10,320 passes (rounded up).
4. Estimate the time it takes to make one pass:
- This will depend on the speed of the mower and the efficiency of the operator. Since we don't have specific information about this, let's assume it takes 5 minutes to make one pass.
5. Calculate the total time required:
- Multiply the time taken for one pass by the number of passes required. In this case, it would be 5 minutes/pass * 10,320 passes = approximately 51,600 minutes.
6. Convert the total time to hours:
- Divide the total time in minutes by 60 to convert it to hours. In this case, it would be 51,600 minutes / 60 = 860 hours.
Using this estimate, you can now calculate the labor cost by multiplying the number of hours (860) by the labor cost per hour ($15). Therefore, the labor cost for mowing the grass would be $15 * 860 hours = $12,900.
It's important to note that this is just an estimate based on the given variables and assumptions. The actual time to mow the grass may vary depending on factors such as the terrain, obstacles, and the skill of the operator.