The rule
direct: x = b × c ÷ a · inverse: x = a × b ÷ c
Why it works
In a direct proportion the ratio between the quantities stays constant, so doubling one doubles the other. In an inverse proportion the product stays constant instead: doubling one halves the other. Which one applies is a question about the situation, not about the numbers.
How to do it by hand
- Decide whether the relationship is direct or inverse
- For direct: cross-multiply and divide by the first value
- For inverse: multiply the first pair and divide by the third value
- Check the answer moves in the direction you expect
What is worth knowing
Choosing the wrong type is the only real error here, and it is a modelling mistake rather than an arithmetic one. More workers means less time, so that is inverse; more workers means more output, so that is direct. Neither is a property of the numbers. A useful sanity check: work out what the answer should roughly be before calculating, and if the result moves the other way, you picked the wrong type. Note too that many real relationships are neither — doubling the workers rarely halves the time exactly, because coordination costs grow.