Find a Rate for One Unit

Supplied materials

• Paper or a note app.
• Fictional pump output: 18 cups in 3 minutes at a constant rate. No pump or mixing is needed.

Learn the idea

A unit rate describes an amount for one unit of another quantity. Divide the cup total by the minutes: cups ÷ minutes gives cups per minute. Keep the units in that order because minutes per cup would answer a different question.

The constant-rate assumption lets us multiply the unit rate by a new duration. It is supplied for this pretend pump; one observed total alone would not prove that a real pump always has the same rate. Check the result by rebuilding the given total.

1. Label the pair as 18 cups and 3 minutes.
2. Divide 18 by 3 and write 6 cups per minute.
3. Check 6 × 3 = 18, then find the output in 5 minutes.

Check your reasoning

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Take it further

For that second pump, change the duration to 6 minutes. Its output is 7 × 6 = 42 cups under the supplied constant-rate assumption.

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