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Math problem set Grade 7 Science

Marchford's Water Loss Audit: Percent Lost Between Plant and Tap

Ten problems comparing what a fictional city's plant produces with what its meters record, finding the percent lost to leaks and what a repair program recovers.

Objectives

  1. Students will calculate daily water loss as a percent of the water a plant produces.
  2. Students will convert between million gallons per day, gallons per minute, and gallons per day.
  3. Students will explain how a leak survey reduces both cost and river withdrawals.

Vocabulary

Non-revenue water
Water that a utility treats and pumps but never gets paid for. Most of it escapes through leaks in old pipes, and some is lost to broken meters or theft.
Water main
A big underground pipe that carries drinking water beneath the streets to a neighborhood. Smaller service lines branch off it to reach each building.

Also: water loss, leak survey, million gallons per day

Teacher overview

Every utility treats more water than its customers ever pay for, because some of it leaks out of old pipes before it reaches a meter. Utilities track that gap in a water loss audit, comparing what the plant produced with what customer meters recorded. This set follows the fictional city of Marchford, whose plant produces 4.5 MGD while its meters add up to 3.6 MGD. Teaching note: students often divide the loss by the metered use rather than by the water produced, which overstates the percent lost. Insisting that the denominator be the plant's production keeps problem 2 and problem 8 consistent with how a real audit is reported.

Marchford's Water Loss Audit: Percent Lost Between Plant and Tap — Grade 7 Science
Name: ____________________________ Date: ______________

Problems

The city of Marchford treats river water at one plant. Last month the plant produced 4.5 MGD, meaning 4,500,000 gallons per day, while all customer meters together recorded 3.6 MGD, or 3,600,000 gallons per day. Treating and pumping water costs the city $1.10 for every 1,000 gallons in this scenario. One MGD equals 694 gallons per minute, and a day holds 1,440 minutes.

  1. How many gallons of water does Marchford lose each day?
  2. What percent of the water the plant produced is lost? Use the production figure as the whole.
  3. How many gallons does Marchford lose in a 365-day year?
  4. What does one day of lost water cost the city to treat and pump?
  5. On average, how many gallons per minute does the plant produce? Use 694 gallons per minute for each MGD.
  6. A leak survey finds one cracked main losing 40 gallons per minute. How many gallons does that single leak waste per day?
  7. What percent of the city's daily loss comes from that one cracked main? Round to the nearest tenth of a percent.
  8. Crews repair enough leaks to cut the daily loss to 600,000 gallons per day. What percent of the plant's production is lost now? Round to the nearest tenth of a percent.
  9. Compare the loss before and after the repairs. By what percent did the daily loss decrease? Round to the nearest tenth of a percent.
  10. Marchford wants to find the next set of leaks without digging up every street. Describe one way the city could monitor its system to narrow the search, and explain what pattern in the data would point to a leak.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 900,000 gallons per day.
    4,500,000 gallons produced minus 3,600,000 gallons metered equals 900,000 gallons lost each day.
  2. Answer: 20 percent.
    900,000 divided by 4,500,000 equals 0.20, which is 20 percent of the water produced.
  3. Answer: 328,500,000 gallons.
    900,000 gallons per day times 365 days equals 328,500,000 gallons in a year.
  4. Answer: $990.
    900,000 gallons divided by 1,000 equals 900 units of a thousand gallons, and 900 times $1.10 equals $990 per day.
  5. Answer: 3,123 gallons per minute.
    4.5 MGD times 694 gallons per minute for each MGD equals 3,123 gallons per minute.
  6. Answer: 57,600 gallons per day.
    40 gallons per minute times 1,440 minutes per day equals 57,600 gallons per day.
  7. Answer: 6.4 percent.
    57,600 divided by 900,000 equals 0.064, which is 6.4 percent of the daily loss.
  8. Answer: 13.3 percent.
    600,000 divided by 4,500,000 equals 0.1333, which rounds to 13.3 percent of production.
  9. Answer: 33.3 percent.
    The loss fell by 900,000 minus 600,000, which is 300,000 gallons per day. Then 300,000 divided by the original 900,000 equals 0.333, a decrease of 33.3 percent.
  10. Answer: Accept any workable monitoring method with a stated signal.
    Strong answers install meters on separate districts and compare each district's overnight flow, since water still moving at 3 a.m. when few people are awake points to a leak. Accept pressure monitoring, acoustic listening on mains, or comparing each district's metered use against the water sent into it.

Differentiation

Support

Give these students a bar model showing the city of Marchford's production split into metered use and loss, with the 900,000 gallon piece already labeled. Provide problem 2 worked out so the production figure is clearly established as the denominator for problem 8, and point out that problem 9 compares the new loss with the original loss instead.

Extension

Have students calculate what a full year of the repaired loss costs the city of Marchford to treat, then compare that figure with the cost of the loss before repairs and state how much the repair program saves in a year.

ELL supports

Preteach produced, metered, and lost with a simple diagram of the city of Marchford showing water leaving the plant, water arriving at houses, and water escaping through a broken pipe. Provide a sentence frame for problem 10: "I would measure ___ at night, because a leak would make that number ___."

Extensions

Students can look up whether their own utility publishes a water loss or non-revenue water figure in its annual report, then compare that percent with the 20 percent the city of Marchford started with.