Math 1030 Working in The Yard
Math 1030 Working in The Yard
Math 1030 Working in The Yard
9/21/18
MATH 1030-414-809
Oremus
For this project, we were given the task of determining the best option for a
hypothetical “neighbor” who is doing a yard project. Would he be better off hauling the
dirt he needs for the project himself, or would it be better to have the store deliver it to
his house for him? This was a multilayered problem that could only be solved by
working through a series of subproblems. Getting any of these subproblems wrong
would drastically affect the outcome of the larger problem, so hopefully I managed to
avoid making any egregious mistakes along the way!
The first thing that needed to be done was to determine how much dirt my
neighbor will need for the project. In order to accomplish this, I would need to figure out
the total area of his yard. First, I divided his yard into 5 different sections and, using the
dimensions provided on the diagram, I came up with the following equations to
determine the area of each section of the yard:
Once I knew the square footage of each section of the yard, I simply added them
all together to get a total area of 9,115 square feet. With this information, I could now
find out how much soil my neighbor would need to cover that area with 4 inches of soil.
First, I needed to convert the 4 inches of soil into feet, so that the units of measure
would be equal: 4 inches is 4/12 of a foot, or about 0.33 of a foot. Then, using the
formula for volume (v=lwh), I calculated the volume of soil my neighbor needed as
follows:
So now I knew how much topsoil my neighbor needed in cubic feet, but because
the store sells the topsoil in increments of ¼ of a yard, I would need to convert my total,
yet again, into cubic yards in order to keep the units of measure equal. Then, once I
figured out how much soil my neighbor would need in cubic yards, I would need to
round that total up to the next ¼ yard, since that is how the soil is sold.
After figuring out the total amount of soil my neighbor would be needing for his
project, it was now time to determine the best option to transport it to his house. The
first option that I explored was to have him haul all of the dirt in his own truck. His truck
bed measures 80 inches long, 69 inches wide, and 20 inches tall. To find out how much
soil his truck could carry at a time, I used the formula for volume again:
Then needed to convert that volume from cubic inches into cubic yards:
So according to these calculations, the truck bed would only be able to carry 2.37
cubic yards of dirt at a time. This would mean that in order to haul 111.5 yards of dirt,
my neighbor would have to make 47 trips to and from the store in his truck. That
would be enough to deter me, but in order to make a fully informed decision, I still
needed to pin down how much gas would cost for those 47 trips to the store. His truck
averages 17 miles per gallon, and the store is 9 miles away, so that would mean that it
would be an 18 mile drive there and back. Gas is currently selling at $3.79 per gallon,
so:
18 miles x 1 gallon x $3.79 = $4.01 for each trip to and from the store
17 miles gallon
So the total cost of gas for my neighbor to drive his truck to and from the
store 47 times would be $188.61. Now, to me, that seems like a lot of time, a lot of
money, and a whole lot of work! My neighbor does, however, have another option. The
store will deliver the dirt to his house for $30 per load, and their truck can deliver 18
Haley Hobson
9/21/18
MATH 1030-414-809
Oremus
cubic yards at a time. This means that they would be able to haul 111.5 yards of dirt to
his house in 6.19 trips…but then that 6.19 would have to be rounded up to 7 trips total,
which would cost my neighbor $210. That means that the store delivery would be
more expensive than hauling the dirt in his own truck by $21.39.
But there is still yet another option. Option #3 would be for my neighbor to have
the store deliver six loads of the dirt for him, and then haul the remaining .19 of a load
himself. So to break that down, if he had the store deliver six truckloads of 18-cubic-
yards of dirt, then that would be 108 cubic yards being delivered for $180. He would
then have a remaining 3.5 cubic yards left that he would need to haul himself. Because
his truck bed can only carry 2.37 cubic yards at a time, he would need to transport those
remaining 3.5 cubic yards in two loads, which would cost him an additional $8.02 in gas.
So this option would bring him to a total of $188.02, which is 59 cents cheaper
than hauling all of the dirt himself, and $21.98 cheaper than having all 111.5 cubic
yards delivered by the store.