Inverse or indirect proportion is a relationship between two variables where an increase in one variable leads to a decrease in the other variable, and vice versa.
- Inverse proportion is a relationship between two variables where an increase in one variable leads to a decrease in the other variable, and vice versa.
- It can be represented mathematically as y = k/x, where y and x are the variables and k is a constant.
- To solve inverse proportion problems, we can use the formula y = k/x.
- Identify the variables involved and assign them as y and x.
- Determine the constant of proportionality, k, by using the given values.
- Substitute the values into the formula and solve for the unknown variable.
As the number of workers increases, the time taken to complete the task decreases.
For example, if it takes 10 workers 5 hours to complete a task, then it would take 20 workers 2.5 hours to complete the same task.
This example demonstrates the inverse proportion between the number of workers and the time taken to complete the task.
As the speed increases, the time taken to travel the distance decreases.
For instance, if a car travels at a speed of 60 km/h, it would take 2 hours to cover a distance of 120 km.
However, if the speed increases to 80 km/h, it would only take 1.5 hours to cover the same distance.
This example illustrates the inverse proportion between speed and time taken to travel a distance.
- If it takes 8 workers 6 hours to complete a task, how long would it take 12 workers to complete the same task?
- Here, the number of workers (x) is inversely proportional to the time taken (y).
- We can set up the equation as y = k/x.
- Substitute the given values: 6 = k/8.
- Solve for k: k = 48.
- Now, substitute the new value of k and the given value of x into the equation: y = 48/12.
- Simplify: y = 4.
- Therefore, it would take 12 workers 4 hours to complete the task.
Step 1: Identify the variables involved. In this case, the variables are the number of men and the number of days
Let x be the number of days it would take for 2 men to build the wall
Step 2: Set up the inverse proportion equation. The product of the number of men and the number of days should remain the same
8 men 5 days =2 men x days
Step 3: Solve for the missing variable
40 =2x
Dividing both sides by2, we get:20 = x
Therefore, it would take 2 men 20 days to build the wall
Step 1: Identify the variables involved. In this case, the variables are the number of workers and the number of days
Let x be the number of days it would take for 9 workers to complete the project
Step 2: Set up the inverse proportion equation
6 workers 10 days =9 workers x days
Step 3: Solve for the missing variable
60 =9x
Dividing both sides by9, we get: x =6.67
So, it would take approximately 6.67 days for 9 workers to complete the project
Step 1: Identify the variables involved. In this case, the variables are the distance traveled and the time taken
Let x be the time taken to travel480 miles
Step 2: Set up the inverse proportion equation
240 miles 4 hours =480 miles x hours
Step3: Solve for the missing variable
960 =480x
Dividing both sides by 480, we get: x =2
In the end, it would take 2 hours to travel 480 miles
Step1: Identify the variables involved. In this case, the variables are the number of workers and the number of days
Let x be the number of workers needed to paint the house in4 days
Step 2: Set up the inverse proportion equation
12 workers 6 days = x workers 4 days
Step3: Solve for the missing variable
72 =4x
Dividing both sides by4, we get:x =18
Hence, 18 workers would be needed to paint the same house in 4 days.
