Answer:
The relation between time and distance is a proportional relationship.
Step-by-step explanation:
Given:
Relation between travel time and distance is given as:
At 2 hours of travel time, distance traveled is 150 miles.
At 3 hours of travel time, distance traveled is 225 miles.
At 4 hours of travel time, distance traveled is 300 miles.
At 5 hours of travel time, distance traveled is 375 miles.
At 6 hours of travel time, distance traveled is 450 miles.
Taking 't' for travel time and 'd' for distance traveled, the above relation expressed in the form of a table is given as:
Time (t) in hours Distance (d) in miles
2 150
3 225
4 300
5 375
6 450
Now, finding the ratio of each of the given quantities, we get:
![\frac{150\ mi}{2\ h}=75\ mi/h\\\\\frac{225\ mi}{3\ h}=75\ mi/h\\\\\frac{300\ mi}{4\ h}=75\ mi/h\\\\\frac{375\ mi}{5\ h}=75\ mi/h\\\\\frac{450\ mi}{6\ h}=75\ mi/h](https://tex.z-dn.net/?f=%5Cfrac%7B150%5C%20mi%7D%7B2%5C%20h%7D%3D75%5C%20mi%2Fh%5C%5C%5C%5C%5Cfrac%7B225%5C%20mi%7D%7B3%5C%20h%7D%3D75%5C%20mi%2Fh%5C%5C%5C%5C%5Cfrac%7B300%5C%20mi%7D%7B4%5C%20h%7D%3D75%5C%20mi%2Fh%5C%5C%5C%5C%5Cfrac%7B375%5C%20mi%7D%7B5%5C%20h%7D%3D75%5C%20mi%2Fh%5C%5C%5C%5C%5Cfrac%7B450%5C%20mi%7D%7B6%5C%20h%7D%3D75%5C%20mi%2Fh)
Hence, we see that the ratio of the time traveled and distance covered is a constant. So, the relation between the two is a proportional relationship and the constant of proportionality is the constant speed of Kent.