The distance between two cities is 180 km. The distance was covered by a car at a rate of 50 km/h, by a bus at 45 km/h, by a truck at 40 km/h, and by a bicycle at 25 km/h. How long did each take to travel the entire distance? Are speed and time directly proportional or inversely proportional? What is the constant of variation?

Step-by-step explanation:

The distance between two cities is 180 km.

Speed = distance/time

Time = distance / speed

This distance was covered by a car at a rate of 50 km/h

Time taken by the car to cover this distance of 180km

= 180/50 = 3.6 hours

This distance was covered by a bus at 45 km/h

Time taken by the bus to cover this distance of 180km

= 180/45 = 4 hours

This distance was covered by a truck at 40 km/h

Time taken by the truck to cover this distance of 180km

= 180/40 = 4.5 hours

This distance was covered by a bicycle at 25 km/h

Time taken by the truck to cover this distance of 180km

= 180/25 = 7.2 hours

Therefore,

speed and time are directly proportional.

Speed, s is inversely proportional to time, t

Introducing constant of variation, k

s = k/t

When s = 25, t = 7.2

25 = k/7.2

k = 7.2 * 25 = 180

So

s = 180/k

s=180/k