## Thursday, February 11, 2010

### Water water everywhere, Part 2

More water today.
I forgot to include figuring out the bill in yesterday's post on water. This is one good reason for studying math in school - utility bills are always complicated - it's not like buying a gallon of milk!
Water isn't free but in the United States it isn't very expensive either.  Most cities monitor the amount consumed, but a few have fixed prices per month and don't charge based on how much you use.
Here are the prices for the water that appear on my water bill:

\$35.42 Basic fee for having water service at a single-family house
PLUS
\$ 3.29 per Hundred Cubic Feet of water, from 0-14 14 HCF
\$ 3.57 per HCF for the next 14 HCF used (from 14-28 HCF)
\$ 4.01 per HCF for all water used (over 28 HCF)

My average bill for the past few years is under 10 HCF. Last month it showed 29 HCF.

That's enough of the facts, now to the math questions!

How much did it cost for the water?

\$35.42 + (14 x 3.29) + (14 x 3.57) + (1 x 4.01) = \$35.42 + 46.06 + 49.98 + 4.01 = \$135.47

How much is that per gallon?

29 x 748 = 21,692 gallons so \$135.47 ÷ 21692 = \$.0062 or about 2/3 of 1¢ per gallon.

We normally consume 9 HCF per 60 day billing period. What is the price of that water?

\$35.42 + (9 x 3.29) = \$35.42 + 29.61 = \$65.03

How much is that per gallon?

9 x 748 = 6732 gallons so \$65.03 ÷ 6732 = \$.0096 or about 1¢ per gallon.

The cost per gallon is higher because the basic fee is a much greater proportion of the bill and is spread out over fewer gallons.

What would the cost per gallon be without the basic fee?

\$29.61 ÷ 6732 =  \$.0043 or less than half the price that we pay including the fee.

There are other charges on the bill too, for sewer service and storm drains, but they don't impact the price of the water we consume.