This holiday weekend, Sandeep is going to Chicago to shop and see a baseball game. To avoid traffic, Sandeep decides to take the train. There is a proportional relationship between the time (in minutes) Sandeep spends riding the train, x, and the distance he travels (in miles), y.

Question

In 6 minutes, his train travels 9 miles. Write the equation for the relationship between x and y.

Answer 1

To find the equation for the proportional relationship between x (time in minutes) and y (distance in miles), we can set up a ratio.

The ratio of time to distance is the same for each point. In this case, the ratio is:

6 minutes : 9 miles

We can simplify this ratio by dividing both the time and distance by their greatest common factor, which is 3:

2 minutes : 3 miles

This simplified ratio shows that for every 2 minutes Sandeep spends riding the train, he travels 3 miles.

Therefore, the equation for the relationship between x and y is:

y = (3/2)x