Question

In: Advanced Math

There was a maths tutoring organisation called Pony Lovers’ Maths (PLM), which provides tuition for children...

There was a maths tutoring organisation called Pony Lovers’ Maths (PLM), which provides tuition for children in school-based mathematics by using ponies as the basis for most of the calculations. This business is a not-for-profit social enterprise. The classroom will house a maximum of 7 people at a time (6 children and 1 teacher) for 3 hours each work day (5 days per week) during school term and holiday periods, but NOT on Public Holidays (10 working days per year). That is, 50 weeks per year.
Part of the workplace health and safety (WHS) requirements to operate is to make available toilet facilities. Also, the Child Protection Act 1999 of Queensland1 requirement is to require for all children to be supervised while that present on the premises. Although there are toilet facilities in another building about 100 metres away in another building, the teacher needs to remain with the other children. Consequently, PLM needs to consider the cost of building a toilet within PLM complex. The classroom and 2 stables has a total roof area of 16 metres long by 6 metres wide. The full roof area is used for collecting rainwater that fills a 25,000 litre tank. There is no other source of water for the building. The Toowoomba Regional Council does not provide sewerage to the site due to its distance away from the city. The building has solar-generated electricity that is backed-up by the electricity grid when the solar panels are not in use at night.
OPTION 1: to build a water closet toilet (the type of toilet normally used in Australian buildings). Because there is no sewerage provided by the council, a septic system (provided by eco-safe waste water treatment) would need to be purchased and installed for $12,500, and the cost of running the electrical pump is around $30 per year (based on non-solar sources). The Eco-safe system is treated by J & K Wastewater services for $250 each year, plus an average of $60 each year for replacement parts and maintenance. The water from this wastewater tank is not suitable for drinking but can be used to irrigate the paddock and generate grass growth. This will reduce the amount of money needed to buy packaged horse-feed, to the value of $225 per year on average.
The link below gives further information.
https://www.ecosafe.com.au/
OPTION 2: to build an Earth closet toilet; a self-contained self-composting, 4 chamber toilet at a cost of $2,254. The system uses a 12 volt/5 Watt fan to keep odours away. This 5 Watt per hour fan runs at all times, and is charged at 30 cents per KWh during the 12 hours of night when solar panels are not operating. Installment also requires the installment of an odour vent pipe ($80 cost plus $100 to install) and an underground drain and gravel pit for draining the liquid waste ($600 total cost of digging, gravel, parts plus installation). The gravel pit must be maintained and not have any additional soil over the pit, which will reduce the usefulness of this area of land. Professional maintenance will cost $200 each year.
In addition, you will need to include the cost of one pack of “Nature Quick Microbes” at $18 for each chamber of the system. These Microbes will need to be added to each chamber twice each year. You will also need 2 bottles a year of “Nature Flush Enzymes concentrate” for $33 each. The link that describes more about this system is given below. (You should select the 4 chamber option to see the price of $2,254 for “Nature Loo Excelet with Chamber Screen” in the link in Footnote 2, below)2:

Statistic Element                                                     January   February   March   April   May   June   July   August   September   October   November   December
Mean rainfall (mm) for years 1869 to 2007             132.1        121.1        94.6     61.9   58.4   56.8     52      39.5        46.7             72.2         89.5             120
Other Information is Below:
Litres per sq. metre of roofing for 1mm of rain           1
Sq. metres area of roof                                              96
Monthly drinking water usage for horses (Litres (L)) 3200 L
Other water usage per month (Litres (L))                   1000 L
Water usage Per Year for flushing toilet in Waste Water System

                                                                                   35,000 L
Rainwater tank capacity (Litres (L))                           25,000 L
Beginning volume of rainwater as at 1 October (Litres (L)) 70%
                                                                                   17,500 L
Using the accepted rainwater collection ratio of 1 millimetre (mm) of rainwater creates 1 litre of rainwater collection per square metre of roofing and PLM’s buildings floor area is 96 square metres, calculate the potential average monthly rainwater collection assuming there is an average monthly rainfall of 79 mm.

2. Calculate the costs to set up each of the 2 toilet system options AND to run the system for the first 12 months after installation.
(5 marks for water closet system; 5 marks for Earth closet system = 10 marks)

Solutions

Expert Solution

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Av. Rainfall
Mean rainfall (mm) 132.1 121.1 94.6 61.9 58.4 56.8 52 39.5 46.7 72.2 89.5 120 78.73333333

  average monthly rainfall = 79 mm.

1. Given that the accepted rainwater collection ratio of 1 millimetre (mm) of rainwater collection per square metre of roofing=1 litre then 76 millimetre (mm) of rainwater collection 96 square metre of roofing=1 litre =76 X 96=7296 L

2.The costs to set up each of the 2 toilet system options AND to run the system for the first 12 months after installation.

Option 1

to build a water closet toilet

A. A septic system (provided by eco-safe waste water treatment) would need to be purchased and installed for $12,500,

B. The cost of running the electrical pump is around $30 per year (based on non-solar sources).

C. The Eco-safe system is treated by J & K Wastewater services for $250 each year, plus an average of $60 each year for replacement parts and maintenance.

D. The water from this wastewater tank is not suitable for drinking but can be used to irrigate the paddock and generate grass growth. This will reduce the amount of money needed to buy packaged horse-feed, to the value of $225 per year on average.

The costs to set up each of the 2 toilet system options AND to run the system for the first 12 months after installation.

=2($12,500+ $30+$250+$60-$225)=$25230

B) to build an Earth closet toilet;

a self-contained self-composting,

4 chamber toilet at a cost of $2,254.

The system uses a 12 volt/5 Watt fan to keep odours away.

This 5 Watt per hour fan runs at all times, and is charged at 30 cents per KWh during the 12 hours of night when solar panels are not operating.

Installment also requires the installment of an odour vent pipe ($80 cost plus $100 to install) and an underground drain and gravel pit for draining the liquid waste ($600 total cost of digging, gravel, parts plus installation).

The gravel pit must be maintained and not have any additional soil over the pit, which will reduce the usefulness of this area of land. Professional maintenance will cost $200 each year.


In addition, you will need to include the cost of one pack of “Nature Quick Microbes” at $18 for each chamber of the system. These Microbes will need to be added to each chamber twice each year.

You will also need 2 bottles a year of “Nature Flush Enzymes concentrate” for $33 each.

The costs to set up each of the 2 toilet system options AND to run the system for the first 12 months after installation.

=2($2,254+((5 X 12 x 50 X 7)(.30/1000))+$80+ $100+$600+$200+2(4 x $18) +(4 x $33) )=$7296.6


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