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Chapter 1: Problem 76

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 ft. An acre is 4840 yd. 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

Expert verified
(a) The cost of desalinated water per liter is \(\frac{\$1950}{(4840 \times (\frac{0.9144}{1})^2 \times \frac{0.3048}{1}) \times 1000}\) dollars per liter. (b) The cost per day for one household using only desalinated water is \(\frac{\$1950}{2 \times 365}\) dollars per day.

Step by step solution

01

Convert acre-foot to liters

We know that 1 acre-foot = 4840 yd^2 * 1 ft (depth), and we should convert it to liters. First, let's convert the volume from cubic yards to cubic meters: 1 yd = 0.9144 m, so 1 ft = 0.3048 m Thus, we can calculate the volume of an acre-foot in cubic meters: \[4840 \text{ yd}^2 \times 1 \text{ ft} \times (\frac{0.9144 \text{ m}}{1 \text{ yd}})^2 \times \frac{0.3048 \text{ m}}{1 \text{ ft}}\]
02

Calculate the cost of desalinated water per liter

Now we know the volume of an acre-foot in cubic meters. We will convert it to liters (1 m^3 = 1000 L) and then calculate the cost of desalinated water per liter. \(Cost~per~liter = \frac{\$1950}{V}\), where V is the volume of an acre-foot in liters.
03

Calculate the daily water consumption of a household

From the problem, 1 acre-foot of water is enough to supply two typical households for 1.00 year. We will find the amount of water consumed by one household daily. \(Daily~Water~Consumption = \frac{V}{2 \times 365}\)
04

Calculate the cost for one household per day

Finally, we can calculate the cost of desalinated water for one household per day using cost per liter and daily water consumption: \(Cost~per~day = Cost~per~liter \times Daily~Water~Consumption\)

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