He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this.
Here is (most of) the information you asked for:
Is he redoing the whole yard or just the front?
He's redoing the whole yard
How much topsoil does he need?
I'm not sure, you'll have to figure that out. Remember he's putting a new 4 inch layer down over all the area currently covered by grass in the overhead picture above.
How big is the yard?
I'm not sure, but you can probably estimate it using the overhead picture.
What kind of pickup truck does he drive?
A 2003 Ford F-150 XL.
How much can the pickup carry?
The truck bed is 80 inches long, 69 inches wide, and 20 inches tall.
How much is the delivery charge?
$30 per truckload on top of the soil cost. Each truckload can deliver up to 18 cubic yards.
How much does the topsoil cost?
$18 per cubic yard (sold in 1/4 yard increments).
How far is the soil store?
It is 9 miles away. It takes about 20 minutes to drive there.
What gas mileage does the pickup truck get?
It averages 17 miles to the gallon.
What is the current gas cost?
Assume it's $3.79/gallon.
Using this information, figure out whether my neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery?
Detail all your assumptions and calculations, and clearly write out your final conclusions.
To determine whether your neighbor should pick up the soil himself or pay for delivery, we will calculate the cost and effort for both options. Here is the breakdown:
1. Calculate the amount of topsoil needed:
To calculate the area of the yard, we can estimate using the overhead picture. Measure the length and width of the yard on the picture and multiply them to get the approximate square footage.
For example, let's assume the yard is approximately 50 feet long and 30 feet wide, which gives us an area of 1,500 square feet.
To convert the area from square feet to cubic yards (the unit in which topsoil is sold), we need to consider the desired 4-inch depth. Divide the area by 9 (since there are 9 square feet in a square yard) and then multiply it by 4 (to account for the desired thickness in inches) and divide it by 12 (to convert inches to feet).
In this case, (1,500 sq ft / 9) * (4/12) = 666.67 cubic feet.
To convert cubic feet to cubic yards, divide the cubic feet by 27 (since there are 27 cubic feet in a cubic yard).
In this case, 666.67 cu ft / 27 = 24.69 cubic yards (rounded to two decimal places).
Therefore, your neighbor will need approximately 24.69 cubic yards of topsoil.
2. Calculate the cost and effort for picking up the soil:
Since the neighbor will be using a pickup truck, we need to calculate the number of trips required based on the truck's capacity.
The truck bed can hold 80 inches (length) * 69 inches (width) * 20 inches (height) = 110,400 cubic inches.
To convert cubic inches to cubic yards, divide by 46,656 (since there are 46,656 cubic inches in a cubic yard).
In this case, 110,400 cu in / 46,656 = 2.37 cubic yards (rounded to two decimal places).
Since each trip can only carry 2.37 cubic yards, your neighbor will need to make approximately 24.69 cubic yards / 2.37 cubic yards per trip = 10.41 trips.
Calculating the cost of gas for the round trip:
The distance to the soil store is 9 miles each way, so the total distance traveled per trip is 9 miles * 2 = 18 miles.
On average, the truck gets 17 miles per gallon, so the number of gallons needed per trip is 18 miles / 17 miles per gallon = 1.06 gallons.
The cost of gas per trip is 1.06 gallons * $3.79 per gallon = $4.02.
Calculating the total cost for picking up the soil:
The cost of the topsoil is $18 per cubic yard, and your neighbor needs 24.69 cubic yards.
Therefore, the cost of the topsoil will be 24.69 cubic yards * $18 per cubic yard = $444.42.
Adding the gas cost to the total cost of topsoil, the final cost for picking up the soil is $444.42 + $4.02 = $448.44.
3. Calculate the cost and effort for delivery:
The delivery charge is $30 per truckload, and each truckload can carry up to 18 cubic yards.
Since your neighbor needs 24.69 cubic yards, he will require 24.69 cubic yards / 18 cubic yards per truckload = 1.37 truckloads.
Calculating the total cost for delivery:
The cost of the topsoil is $18 per cubic yard, and your neighbor needs 24.69 cubic yards.
Therefore, the cost of the topsoil will be 24.69 cubic yards * $18 per cubic yard = $444.42.
Adding the delivery charge to the total cost of topsoil, the final cost for delivery is $444.42 + $30 = $474.42.
Conclusion:
Based on the calculations, it is more cost-effective for your neighbor to pick up the soil himself. The total cost for picking up the soil in his pickup truck is $448.44, whereas the cost for delivery is $474.42. By picking up the soil, he would save approximately $25.98.
However, it is important to note that picking up the soil requires extra effort and multiple trips, which may not be convenient for everyone. Your neighbor should consider both the cost and effort required before making a decision.
To determine whether your neighbor will save money by picking up the soil himself or paying for delivery, we will need to calculate the costs involved in each scenario. Let's break down the calculations step by step:
1. Calculate the amount of topsoil needed:
- We know that your neighbor wants to add a new 4-inch layer of topsoil over the entire area currently covered by grass.
- To estimate the yard's size, we can use the overhead picture and assume it's rectangular. Identify any measurements available and calculate the missing ones. Make sure to account for any non-yard areas in the picture.
- Once you determine the yard's dimensions, convert the width and length to feet if necessary and multiply them by 4 inches to get the volume in cubic feet.
- Convert the cubic feet to cubic yards by dividing by 27 (since 1 cubic yard is equal to 27 cubic feet).
2. Calculate the number of truckloads needed:
- Each truckload can carry a maximum of 18 cubic yards.
- Divide the total amount of topsoil needed by 18 to find out how many truckloads are required.
3. Calculate the cost of the topsoil:
- The topsoil costs $18 per cubic yard.
- Multiply the total number of cubic yards needed by $18 to get the cost of the topsoil.
4. Calculate the cost of pickup truck transportation:
- Determine the distance to the soil store, which is 9 miles away.
- Divide the distance by the pickup truck's gas mileage (17 miles to the gallon) to find out how many gallons of gas will be used for the round trip.
- Multiply the gallons of gas by the current cost per gallon ($3.79) to calculate the cost of gas for the round trip.
5. Compare the total cost of pickup truck transportation to the delivery charge:
- Assess which is more cost-effective: picking up the soil using the pickup truck or paying for the delivery.
- Add the cost of gas for the round trip (from step 4) to the cost of the topsoil (from step 3) to get the total cost of picking up the soil.
- Compare the total cost of picking up the soil to the delivery charge of $30 per truckload.
Based on these calculations, you can determine whether your neighbor should pick up the soil himself or opt for delivery. Make sure to document all your assumptions and calculations and present your final conclusions clearly.