SOLUTION: Time varies inversely with speed if the distance is constant. A trip takes 4 hours at 80 km/h. How long does it take at 64 km/h? Please show me the complete solution. Thanks.

d = r * t    where r=rate, t=time, d=distance
so yes, rearranging to t = d/r "time varies inversely with speed if distance is constant"

The trip is the same distance, no matter what the speed.  Can we find the trip distance?  Yes, from the speed and time information given (4 hrs at 80km/hr):  

d = 4hrs * 80km/hr = 320km

Now we can divide the trip distance by the other speed in order to get the time required:

t = 320km / 64km/hr =  hrs
———————

A 2nd way to do this (although mathematically equivalent) is to use the ratio of the two speeds, essentially it is just a re-grouping the distance calculation, as follows:

 t = (4hrs * 80km/hr) / 64km/hr = 4hrs * (80km/hr / 64km/hr)  = 4hrs * (1.25) = 5 hrs