Question

In the United States, water used for irrigation is measured in acre-feet. An acre-foot of water covers an acre to a depth of exactly \(1 \mathrm{ft}\). An acre is \(4840 \mathrm{yd}^{2}\). An acre-foot is enough water to supply two typical households for 1.00 yr. (a) If desalinated water costs \(\$ 1950\) per acre-foot, how much does desalinated water cost per liter? (b) How much would it cost one household per day if it were the only source of water?

Short answer

(a) Desalinated water costs approximately $0.00158 per liter. (b) The daily cost for one household would be about $2.67 if desalinated water were the only source of water.

Step-by-step solution

Find the volume of one acre-foot in cubic yards

One acre-foot covers an area of 4840 square yards to a depth of 1 ft. So, the volume of one acre-foot can be calculated as followed: \(volume = area \times depth\) Since 1 acre is equal to \(4840\) square yards and 1 ft is equal to \( \frac{1}{3}\) yards, we have: \(volume = 4840\,\mathrm{yd}^2 \times (\frac{1}{3}\,\mathrm{yd}) = 1613.33\, \mathrm{yd}^3\)

Convert cubic yards to liters

We will use the conversion: \(1\, \mathrm{yd}^3 \equiv 764.55\, \mathrm{L}\) So, one acre-foot is equal to: \(1613.33\, \mathrm{yd}^3 \times 764.55\, \mathrm{L/ yd}^3 \approx 1,233,450\, \mathrm{L}\) 2: Calculate cost per liter

Calculate the cost per liter

If desalinated water costs $1950 per acre-foot, the cost per liter can be calculated as: \(\mathrm{Cost\, per\, liter} = \frac{\$1950}{1,233,450 \, \mathrm{L}} \approx \$0.00158 \, \mathrm{per\, liter}\) 3: Calculate daily cost for one household

Calculate the daily water consumption per household

According to the problem, one acre-foot is enough to supply water to two households for one year (365 days). So, the daily water consumption by one household can be calculated as: \(\mathrm{Water\, consumption\, for\, 1\, household} = \frac{1,233,450\, \mathrm{L}}{2 \times 365 \, \mathrm{days}} \approx 1689.17 \, \mathrm{L/day}\)

Calculate daily cost for one household

Now, we can calculate the daily cost for one household using the cost per liter: \(\mathrm{Daily\, cost\, for\, 1\, household} = 1689.17\, \mathrm{L/day} \times \$0.00158\, \mathrm{per\, liter} \approx \$2.67 \, \mathrm{per\, day}\) Answer: (a) Desalinated water costs approximately $0.00158 per liter. (b) The daily cost for one household would be about $2.67 if desalinated water were the only source of water.