Inverse Quantity Math Example 1

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Example 1

easy
If 55 workers can complete a job in 1212 days, how many days will it take 1515 workers (assuming equal work rates)?

Solution

  1. 1
    Total work =5×12=60= 5 \times 12 = 60 worker-days.
  2. 2
    With 1515 workers: days =6015=4= \dfrac{60}{15} = 4 days.
  3. 3
    Alternatively: workers and days are inversely proportional, so 5×12=15×d5 \times 12 = 15 \times d, giving d=4d = 4.

Answer

It will take 44 days.
When two quantities are inversely proportional, their product is constant. More workers means fewer days, and the product (total worker-days) stays the same. The relationship is w×d=kw \times d = k, not w/d=kw/d = k.

About Inverse Quantity

The reciprocal or multiplicative inverse of a quantity, where multiplying a number by its inverse yields one. Inverse quantities appear whenever two measurements are inversely related, so that doubling one halves the other.

Learn more about Inverse Quantity →

More Inverse Quantity Examples

Example 2 medium

The pressure [formula] of a gas varies inversely with its volume [formula] at constant temperature (

Example 3 easy

At [formula] km/h a trip takes [formula] hours. How long does the same trip take at [formula] km/h?

Example 4 medium

Variables [formula] and [formula] are inversely proportional. When [formula], [formula]. Find [formu

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