Inverse proportion is when two quantities change opposite to one another.
As one quantity increases, the other quantity decreases.
When the two quantities are multiplied, the same constant occurs.
A common example of inverse proportion is to calculate the time it takes to do a job with more or fewer workers.
3 talented graffiti artists can paint a wall mural in 10 hours. To paint the same mural on another wall, calculate the time it would take:
(a) 1 artist
(b) 6 artists.
Answer:
(a) Multiplied constant
= 3 artists × 10 hours
= 30 man-hours
Time with 1 artist
= 30 man-hours ÷ 1 artist
= 30 hours
(b) Time with 6 artists
= 30 man-hours ÷ 6 artists
= 5 hours
4 men can build a shed in 20 hours. Calculate how long the same shed would take to build:
(a) if there was 1 man
(b) if there were 5 men.
Answer:
(a) Multiplied constant
= 4 men × 20 hours
= 80 man-hours
Time with 1 man
= 80 man-hours ÷ 1 man
= 80 hours
(b) Time with 5 men
= 80 man-hours ÷ 5 men
= 16 hours
It takes 6 people 8 hours to build a fence around a farm. How long would the same fence have taken to build with 12 people? (Hint: Find the number of hours with only 1 person first.)
Answer
4 hours
Doctors use a Body Mass Index to determine if people are healthy or not. A BMI of 25 is healthy. Less than 25 is underweight. More than 25 is overweight.
Body Mass Index = | Mass in kg |
Height in metres-squared |
Measure your mass in kilograms. Measure your height in metres. Calculate your BMI.
According to the rule above, are you healthy? What problems are there with this rule?
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