Question
A campsite must order all the fresh water it will need tomorrow. The manager's estimates are:
- 20 campers each drink 3 litres.
- Cooking requires another 30 litres.
- Washing dishes uses 50 litres.
- Cleaning the floors requires 40 litres.
The campsite can capture 60% of the dishwashing water after use and reuse that water only for the floors. It cannot be used for drinking, cooking or washing dishes again. Water is reused only once, and all estimated demand must be met.
How many litres of new water must the campsite order? If delivery is available only in sealed 20-litre containers, what is the minimum number of containers?
Get hint
Hint 1
First calculate the floor-cleaning demand that captured dishwater can actually cover.
Check your answer
Solution
Drinking needs \(20\times3=60\) L. Cooking needs 30 L. Dishwashing itself needs 50 L of initially fresh water. Those uses consume \(60+30+50=140\) L of new supply before floor cleaning.
Recovery provides \(0.60\times50=30\) L of dishwater that may be reused only for floors. Since floors need 40 L, they still require \(40-30=10\) L of fresh water. Therefore
\[
W_{\mathrm{new}}=60+30+50+\max(40-30,0)=\boxed{150\text{ L}}.
\]
The same answer follows by balancing total uses: \(60+30+50+40=180\) L of water demand, of which 30 L is met by water already supplied for dishwashing, leaving 150 L of external supply. This recovered 30 L must not be counted again as new water. Nor can it offset drinking or cooking, which require fresh water.
Containers cannot be divided, so the minimum number is \(\lceil150/20\rceil=\boxed{8}\). The site receives 160 L and has 10 L spare if forecasts are exact.
Assumptions
All demands are fixed forecasts for one day and measured in litres.
Only 60% of the 50 L dishwashing use is recoverable; reuse is restricted to floor cleaning and the remainder is lost.
Every container holds 20 L of delivered fresh water; containers cannot be split or purchased fractionally.
Final Answer
150 litres of fresh water; order 8 containers of 20 litres (160 litres delivered).