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Math problem set Grade 7 Math

Salt Fork Booster Station: Combining Two Pumps to Fill a Hilltop Tank

A grade 7 math set on a fictional booster station's two pumps, using proportional reasoning and percent problems to compare fill times and a fill-rate goal.

Objectives

  1. Students will calculate the combined flow rate of two pumps running together.
  2. Students will use flow rate and time to calculate what percent of a tank has filled.
  3. Students will check a combined pump system against a stated fill-percent goal within a time limit.

Vocabulary

Flow rate
Flow rate measures how much water moves past a point in a certain amount of time, like gallons per minute through a garden hose. Bigger pipes and stronger pushes give bigger flow rates.

Also: combined rate, proportional relationship

Teacher overview

The fictional Salt Fork Booster Station pumps water uphill from a low reservoir to the Ridgetop hilltop tank using two pumps that can run separately or together. This problem set has students use each pump's flow rate to find how long the tank takes to fill under different combinations, then check whether the station can meet a stated fill-percent goal within a work shift. A common misconception in this math is assuming that running two pumps together always cuts the fill time exactly in half; the actual combined time depends on the sum of the two pumps' individual flow rates, which only equals a 50 percent time reduction when both pumps move water at the same rate.

Salt Fork Booster Station: Combining Two Pumps to Fill a Hilltop Tank — Grade 7 Math
Name: ____________________________ Date: ______________

Problems

The fictional Ridgetop tank holds 60,000 gallons and starts empty. Pump 1 moves water at a steady 150 gallons per minute (gpm). Pump 2 moves water at a steady 100 gpm.

  1. How many gallons does Pump 1 alone move in 1 hour (60 minutes)?
  2. If only Pump 1 runs continuously, how long would it take, in minutes, to fill the empty 60,000-gallon tank?
  3. Write the combined flow rate, in gpm, when both Pump 1 and Pump 2 run at the same time.
  4. Using your answer to problem 3, how long, in minutes, would it take both pumps running together to fill the empty tank?
  5. Compare your answers to problems 2 and 4. Is the combined fill time exactly half of Pump 1's solo fill time? Explain why or why not, using the two pumps' individual rates.
  6. After running both pumps together for 2 hours (120 minutes), what percent of the tank's 60,000-gallon capacity is full? Round to the nearest whole percent.
  7. The station manager wants the tank at least 90 percent full within a 3-hour (180-minute) shift, using both pumps. Based on the combined rate from problem 3, will the station meet that goal? Show the calculation that supports your answer.
  8. Challenge. A third, identical pump (100 gpm) is installed, so all three pumps can run together. What is the new three-pump combined flow rate, and about how many minutes would it take to fill the empty tank? Round to the nearest minute.

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: 9,000 gal.
    150 gpm × 60 minutes = 9,000 gallons in 1 hour.
  2. Answer: 400 min.
    60,000 gallons ÷ 150 gpm = 400 minutes (6 hours 40 minutes) for Pump 1 alone to fill the tank.
  3. Answer: 250 gpm.
    150 gpm + 100 gpm = 250 gpm combined.
  4. Answer: 240 min.
    60,000 gallons ÷ 250 gpm = 240 minutes (exactly 4 hours) for both pumps together to fill the tank.
  5. Answer: No.
    Half of Pump 1's solo time (400 minutes) would be 200 minutes, but the combined time is 240 minutes. Because Pump 2 (100 gpm) is slower than Pump 1 (150 gpm), adding it does not double the total rate, so the fill time does not drop by exactly half.
  6. Answer: 50 percent.
    120 minutes × 250 gpm = 30,000 gallons. 30,000 ÷ 60,000 × 100 = 50%.
  7. Answer: No.
    180 minutes × 250 gpm = 45,000 gallons. 45,000 ÷ 60,000 × 100 = 75%, which is short of the 90% goal by 15 percentage points.
  8. Answer: 171 min.
    Three-pump combined rate: 150 + 100 + 100 = 350 gpm. 60,000 gallons ÷ 350 gpm ≈ 171.4 minutes, which rounds to 171 minutes (about 2 hours 51 minutes).

Differentiation

Support (below grade level)

Provide a printed table with columns for "Pump combination," "Combined rate (gpm)," and "Time to fill (min)," partially filled in with the Pump 1-alone row completed, so students only need to compute the remaining rows. Allow a calculator for all division steps.

Extension (above grade level)

Ask students to find the minimum combined flow rate, in gpm, the fictional station would need to fill the tank to 90 percent within the original 3-hour shift, and to compare that required rate to the two original pumps' combined rate from problem 3 to see how much more capacity would be needed.

ELL supports

Pre-teach "flow rate" and "combined rate" with a simple visual of two pipes, each labeled with its gpm value, merging into one larger pipe labeled with the sum. Allow problem 5's explanation to be given as a short spoken response to a partner instead of a written paragraph.