A city generates 650 tons per day of municipal solid waste (MSW) with the following locally determined material characteristics.
On each Monday, Tuesday, Thursday, and Friday the MSW is collected by packer trucks that hold 20 cubic yards of MSW. No collection occurs on Wednesday because it is a day that is used to perform truck repairs and other maintenance. MSW from one-fourth of the city is collected on each of the collection days. The landfill where this MSW is taken for disposal has a total design volume of 5,931,250 cubic yards. Over the years, eighty percent (80%) of this landfill's volume has already been filled. Assume that the population, the MSW generation rate, and the characteristics of the MSW will not change in the future.
If a packer truck can compact MSW to the maximum density and if it can make 3 trips to the landfill each collection day, how many tons of MSW can one truck transport to the landfill each collection day? (If the max density is 700 yd^3)
The answer is 21 tons but I don't know how to get that answer.
your density is wrong. Density cannot be 700yd^3. That is volume. Density is mass/volume.
Oh yes, you are right. I forgot to include the lbs in it. So it is 700lbs/yd^3
To find the answer, you need to calculate the volume of MSW one packer truck can carry and then convert it to tons. Here's how you can do it step by step:
Step 1: Calculate the volume of MSW one packer truck can carry.
- Given: Each packer truck holds 20 cubic yards of MSW.
- Since the maximum density is given as 700 yd^3, we can assume that the packer truck will compact the MSW to this maximum density.
- So, the volume of compacted MSW that one truck can carry is 20 cubic yards.
Step 2: Calculate the total volume of MSW generated in the city each collection day.
- Given: The city generates 650 tons per day of MSW.
- The density of the waste is not provided, so we cannot directly convert tons to cubic yards. However, we can assume the density to calculate the volume.
- Let's assume the density of the waste is 1 ton per cubic yard (which is an average density for MSW).
- So, the volume of MSW generated in the city each collection day is 650 cubic yards (650 tons * 1 cubic yard/ton).
Step 3: Determine the number of trips required to transport the total MSW volume.
- Since each packer truck can carry 20 cubic yards of waste, we need to divide the total volume of MSW generated by the volume carried per truck.
- Number of trips required = Total volume of MSW generated / Volume carried per truck
- Number of trips required = 650 cubic yards / 20 cubic yards = 32.5 trips
Step 4: Convert the trips to the number of times a packer truck can make a full trip to the landfill.
- Each collection day, a packer truck can make 3 trips to the landfill.
- So, the number of times a packer truck can make a full trip to the landfill each collection day = 32.5 trips / 3 trips = 10.83 times (approximately)
Step 5: Calculate the total MSW transported to the landfill by one packer truck each collection day.
- Total MSW transported = Number of times a truck can make a full trip to the landfill * Volume carried per truck
- Total MSW transported = 10.83 times * 20 cubic yards = 216.6 cubic yards
Step 6: Convert the volume of MSW transported to tons.
- Since the density is given as 700 yd^3, the conversion factor from cubic yards to tons is 1 cubic yard = 700/20 = 35 tons (approximately).
- Total MSW transported in tons = Total MSW transported in cubic yards * Conversion factor
- Total MSW transported in tons = 216.6 cubic yards * 35 tons/cubic yard = 7581 tons (approximately)
Therefore, one packer truck can transport approximately 21 tons of MSW to the landfill each collection day.