Question

The time t required to travel a fixed distance varies inversely as the speed r. it takes 5h to drive the fixed distance at a speed of 80km/h. how long will it take to drive the same distance at a speed of 70km/h?

Answer 1

Let t be time and r be rate, then if time varies inversely with the rate, the equation is $t= \frac{k}{r}$.  If it takes 5 hours to drive a fixed distance at a rate of 80, we can sub those values in to solve for the constant of variation, k.$5= \frac{k}{80}$.  Solve for k by multiplying 5 and 80 to get that k = 400.  Now let's find a new time t when r is a rate of 70.  We will use that k value to do this: $t= \frac{400}{70}$ and find that it will take 20 hours to drive the distance at 70 mph when it takes 5 hours to drive the distance at 80 mph.  Makes sense that it takes longer to drive a fixed distance when you are going slower.