Speed × time (fixed distance)
- Input
- A=80, B=3, C=100
- Expected output
- X = 2.4
At 80 km/h for 3 h the trip covers 240 km; over the same distance at 100 km/h, the time drops to 2.4 h (2 h 24 min).
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inverse rule of three
In an inverse proportion, the product of the two quantities stays constant: A × B = C × X, so X = A × B / C. It models situations where increasing one quantity makes the other decrease at the same rate, such as speed and time for a fixed distance.
At 80 km/h for 3 h the trip covers 240 km; over the same distance at 100 km/h, the time drops to 2.4 h (2 h 24 min).
3 taps take 10 h; 5 taps keep the product at 30 and finish in 6 h, not by coincidence: 30÷5=6.
Dropping from 5 to 3 painters stretches the deadline from 12 to 20 days, keeping the painters×days product at 60.
In a direct proportion, two quantities grow or shrink together: doubling one doubles the other. You set up A/B = C/X and isolate the unknown with X = B × C / A. For example, if 3 workers produce 6 items per day, 5 workers produce X = 6 × 5 / 3 = 10 items, because more labor yields more output in the same proportion.
Use inverse when increasing one quantity proportionally decreases the other, like speed and time or workers and deadline; if both grow together, like price and quantity, it is direct, and the formula switches from A×B=C×X to A/B=C/X.
Only while the work stays perfectly divisible with no dependency between steps; dropping from 5 to 3 painters stretches the deadline from 12 to 20 days, but sequential tasks, where one step requires the previous one finished, do not follow that same proportion.
Because it represents the fixed physical quantity behind the proportion, like a trip's distance or a tank's volume; in the taps example, the taps×hours product stays at 30 both for 3 taps in 10 h and for 5 taps in 6 h.
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