Additional Math Pages & Resources

Wednesday, February 10, 2010

Water water everywhere, Part 1

I live right next to the ocean. But in a desert. So we have to import our water. The city provides us with water and sends us a bill every 2 months.

Back in November I discovered a leak in one toilet, and a broken pipe in the back garden. I didn't know what the impact of the leaks would be, but we fixed them as soon as we noticed. Then we had 3 sets of visitors over the Christmas holiday time.

When the water bill arrived the amount we were faced with was huge! MUCH greater than we had ever used before.

The meter had been read one week before, and the reading on the bill was 1613.00


I decided to check the meter myself. We found the box in the sidewalk, opened it and took a photo. It says 1614.03 (+.68). If their figures were correct, we had used 1 HCF in the week since the meter was read.

I called the water department and asked some questions. They said we could check to see if there were any leaks, by turning off all water sources, checking the meter, waiting an hour, then checking again. If the meter needle moved, there might be a leak somewhere underground or in a pipe under the house. So we turned off everything and waited.

After a few minutes my wife started washing the dinner dishes. WAIT! I shouted. We're checking the water! Sorry, she said, as we waited some more, tapping our toes impatiently. Finally I took another photo.

The meter now said 1614.03 (+.75). That small movement of the needle must have been my wife filling the kitchen sink. Seems reasonable. So we waited a bit more. No change in the readings, so probably no leaks.

But I was not completely convinced. We were very careful with our use of water for another week, then I checked the meter again.


Now we could see a real change. The meter measured 52 cubic feet, or just about half of a "hundred cubic foot" unit used by our water department.

How could I tell if this is normal water consumption? I checked my previous bills, prior to all the fuss. We have averaged 9-10 HCF for an average billing cycle of two months (60-62 days).

Let's make a number sentence problem from this.

Is 9 HCF over 62 days less than, equal to or greater than .52 HCF over 7 days?

900 ÷ 62 days = 14.5 cubic feet per day
52 ÷ 7  days = 7.43 per day

It's almost exactly half our average from previous months! (Was there a leak then too?)

I think we need a better sample. A bigger one. So let's recheck the figures using the water company reading from two weeks ago. It was then 1613 (roughly) so we now have this calculation:

1614.55-1613.00 = 1.55 HCF  or 155 cubic feet

155 ÷ 14 days = 11.1 cubic feet per day

That's under our normal usage. But reasonable.  Remember it has been raining around here. It was not dry as a bone this January and February. As my poor cat found out ...


Are you wondering how much water is in that strange HCF unit? It's 748 gallons. Now we can ask: How many gallons have we used in 2 weeks?

If 100 cubic feet = 748 gallons, then 1 cubic foot = 7.48 or about 7.5 gallons.

Since we used 11.1 cubic feet per day that's 11.1 x 7.5 = 83.25 gallons of water per day.

That seems like a lot! But indoor water use guidelines for US consumers suggest a maximum of 65 gallons per day per person. With 3 people in our house these past few weeks, our average usage is below those guidelines.

83.25 ÷ 3 = 27.75 gallons per person