A150 km trip was covered by a motorcycle going at an average speed of 75 km/h, by a bus doing 60 km/h, by a truck doing 50 km/h, and by a bicycle doing 20 km/h. are speed and time directly proportional? inversely proportional? what is the constant of variation?

Since speed, S = Distance(D)/ time(t). So, yes, speed and time are inversely proportional. There's an inverse relationship between them. All three have to cover 150km. The relation is given by X = 150/ K where X is the speed and K is the variation constant. If the speed, X, is large, then K is small and if X is small then K is large. The constant of variation which is actually the time for motorcycle, bus, and truck and bicycle given that the travel at speed of 75km/h, 60km/h, 50km/h and 20km/h respectively is K = 150/75, 150/60, 150/50, 150/20 so we have 2h, 2.5h, 3h, 7.5h respectively.