The time t required to drive a centain distance varies inversely with the speed r. If it takes 2 hours to drive the distance at 30 mines per hour how long will it take to drive the same distance at 50 miles per hour
An inversely proportional equation for our set of circumstances looks like this: [tex]t= \frac{k}{r} [/tex]. We have a t value of 2 and an r value of 30, so we will sub those values in and solve for k, the constant of variation. [tex]2= \frac{k}{30} [/tex]. Multiply both sides by 30 to get that k = 60. Now we need to find t when r = 50. We can do this now because we have a value for k. [tex]t= \frac{60}{50} [/tex] and t = 1.2 hours.
