NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Rates and unit comparisons

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A farmer in Wagga Wagga uses a sprinkler system that waters 1500 square metres of farmland in 2 hours and 30 minutes. What is the rate of watering in square metres per minute?

Express your answer as an exact fraction.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The sprinkler waters 1500 square metres in 2 hours and 30 minutes. First, convert the time to minutes because the rate is required in square metres per minute.
  2. 2 hours = 2 × 60 = 120 minutes. Add 30 minutes: 120 + 30 = 150 minutes.
  3. The total area watered is 1500 m² over 150 minutes. The rate is area divided by time.
  4. Rate = 1500 m² ÷ 150 min. Perform the division: 1500 ÷ 150 = 10.
  5. The result is 10 square metres per minute. Express as a fraction: 10/1.
  6. Simplify the fraction 1500/150. Both numerator and denominator are divisible by 150.
  7. 1500 ÷ 150 = 10, 150 ÷ 150 = 1. So, 1500/150 = 10/1.
  8. The fraction 10/1 is already in simplest form. No further simplification is needed.
  9. The rate is 10 square metres per minute. This is an exact value.
  10. Check: 10 m²/min × 150 min = 1500 m². This matches the given area.
  11. The rate of watering is 10 square metres per minute, expressed as the exact fraction 10/1.
  12. Final answer: 10/1 square metres per minute.

Reference answer: 10/1

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