Question

·Kent is driving cross country from Tampa, Florida to Corpus Christi, Texas. He drives at a

constant speed before taking his first rest stop. At 2 hours he has traveled 150 miles, at 3 hours he
has traveled 225 miles, at 4 hours he has traveled 300 miles, at five hours he has traveled 375 miles,
and at 6 hours he has traveled 450 miles, at which time he stops for lunch.
Illustrate the relation between travel time and distance using a table.

Answer 1

The relation between time and distance is a proportional relationship.

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:

`(150\ mi)/(2\ h)=75\ mi/h\\\\(225\ mi)/(3\ h)=75\ mi/h\\\\(300\ mi)/(4\ h)=75\ mi/h\\\\(375\ mi)/(5\ h)=75\ mi/h\\\\(450\ mi)/(6\ h)=75\ mi/h`

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.