What is Inverse Variation

In the given two variables if the value of one variable increases and another one decreases   that is if the values change in opposite manner then it’s said to be inverse variation.
For example if the speed increases the travelling time decreases and if speed decreases the travelling time increases

Inverse variations  occurs  when two variables such as XY are always equation to some constant K ie, one value  decreases and the other value increases

No of workers Days to complete the  work
        15               15
        10               18
         5               20

As the   number of worker decreases the days to complete the work increases.  Here inverse variations occur.

Inverse Variation Formula

Inverse-variation between two variables say  y and x is given by the formula    y  =  k/x
Here the variable K is known as the constant of proportionality.  Y varies inversely with x.
Y varies inversely with x, if there is a nonzero constant k such that xy = k or ,  y  = k/x, where k ≠ 0.
In inverse-variation its seen that , when the value of one  variable increases the value of the other value  decreases in proportion so that the product remains the same always.

Inverse Variation Word Problems

While solving inverse-variation word problems we use the formula ‘y = k/x   or any other variables relevant to the problem. Find the value of ‘k’ which is the constant of proportionality.
Plug in the value of k in the formula y=k/x .  Use the information from the given problem and solve for the variable.  An example problem is solved below.

If a car travels at the rate of 20 miles per hour it takes 1.5 hours to reach its destination.  If the same car travels at the rate of  50 miles per hour  what will be the time taken to reach its destination.

Use  the formula     t  =  k/s  where  t = 1.5 and s = 20 .  Plug in the values of t and s and find k.
         
                                   1.5  = k/20    (multiply by 20 both sides)
                                   K  = 1.5 x 20
                                   K =  30

Substitute the value of ‘k in the  equation   t = k/s
Here   k = 30  and  t  =  50
                                    t = 30/50

                                    t =  0.6 hours
The car takes 0.6 hours if it travels at the speed of 50 miles per hour.    Here it is found that as the speed of the car increases the time taken reduces.  So   there is inverse-variation here.