APES
SOLID AND HAZARDOUS WASTE
MATH PROBLEMS
NAME: __________________
DATE: ______________
Understanding Household solid waste
The table below shows the percentage composition of typical municipal solid waste (MSW)
generated by a household in the United States according to 2007 report by the EPA.
Material
Food scraps
Paper and paperboard
Plastic metals
Metals
Glass
Yard trimmings
Percentage (%)
12.5
32.7
12.1
8.2
5.3
12.8
Consider a household that has four residents and generates four pounds of MSW per day per
person. The tipping fee in their location is $60 per U.S. ton. The household has already
reduced its amount of garbage through reducing and reusing materials, but now wants to
lower the amount further by recycling. The major recyclables in the waste stream of this
household are paper, plastic, glass, and metals.
Use the preceding table and information to answer the following questions.
a) How much MSW does the household generate in a month?( 31 days)
b) How much MSW does the household generate in a year? (365 days)
c) How much does the household pay for tipping fees each year?
d) Approximately how long does it take the household to generate a ton of MSW?
e) If the household decided to compost all of its food scrap, paper, and yard trimmings,
how much would it save on tipping fees each year?
f) If the household decided to recycle all its plastic and glass, how much would it save on
tipping fees each year?
g) How much would the household save if it did both composting and recycling as in e
and f, and how much MSW would it generate a year as a result?
2. Annual precipitation at a landfill in the town of Fremont is 100mm per year, and
50% of this water runs off the landfill without infiltrating the surface. The landfill has a
surface area of 5000m2miles. Underneath the landfill the town installed a leachate
collection system that is 80% effective. Any leachate not collected by the system
enters the surrounding soil and ground water. This leachate contains cadmium and
other toxic metals.
Calculate the volume of water in cubic meters (m3) that infiltrates the landfill per year.
APES
SOLID AND HAZARDOUS WASTE
The county gov't in one Eastern state initiated an aluminum recycling program. Most of the Al is
in the form of beverage cans. In the first year, the county collected 1.4E6 kg of cans (1.4 million).
It takes about 65 cans to make a kg. All communities in the country have curb-side pickup of
recycled materials. On average, each truck makes a 75-km trip to pick up 3500 kg of Al and gets
5.0 km/L fuel economy. Each liter of fuel produces 42 000 kJ of energy. ( 1.4E6=1.4X106)
1. How many cans did the county collect in the first year?
2. How many trips were needed to collect all the cans? Please round up.
3. Calculate how many liters of fuel the trucks used to pick up the cans.
4. How many kilojoules (kJ) of energy were consumed collecting the cans?
5. Making cans from recycled aluminum requires about 180 kJ of energy per can. Calculate the
total energy needed to make cans from recycled aluminum, including the energy used to collect
them.
6. It takes 1520 kJ of energy to make one Al can from bauxite ore. Assuming no other energy is
used, calculate how much energy is needed to make the cans from this virgin ore.
7. Calculate the energy difference between the two methods. How many liters of fuel are saved
by recycling the cans?