Question

The time t required to drive a certain distance varies inversely with the speed r. If it takes 2 hours to drive the distance at 40 miles per hour, how long will it take to drive the same distance at 45 miles per hour? about 1.78 hours 80 hours 2.25 hours 900 hours

Answer 1

If t varies inversely with the speed, the formula for that is  $t= \frac{k}{r}$.  If t = 2 and r = 40, then we can solve for k, the constant of variation.  Multiply both sides by 40 to get  k = 80.  Now we need to find the value for t when r = 45.  Using the k value we just solved for, we will fill in the equation as  $t= \frac{80}{45}$  for a t value of about 1.78 hours