Writing a Formula for an Inversely Proportional Relationship

Recall that multiplying speed by time gives distance. If we let $t$ represent the drive time in hours, and $v$ represent the velocity (speed or rate) at which the tourist drives, then $vt=\text{distance}\text{.}$ Because the distance is fixed at 100 miles, $vt=100$ so $t=\mathrm{100/}v.$ Because time is a function of velocity, we can write $t(v).$

We can see that the constant of variation is 100 and, although we can write the relationship using the negative exponent, it is more common to see it written as a fraction. We say that time varies inversely with velocity.