Constant of Variation

Example 1:

If $y$ varies directly as $x$ and $y=15$ when $x=24$ , find $x$ when $y=25$ .

Find the constant of variation.

To find $x$ , substitute $25$ for $y$ .

$\begin{array}{l}25=\frac{5}{8}x\\ x=40\end{array}$

Example 2:

If it takes $4$ hours at an average speed of $90$ km/h to do a certain journey, how long would it take at $120$ km/h?

Find the constant of variation.

$k$ = speed · time

$k=90\cdot 4=360$

Then,

$\begin{array}{l}\text{time}=\frac{k}{\text{speed}}\\ =\frac{360}{120}\\ =3\text{ hours}.\end{array}$