Question

You are traveling on a bus to camp, which is 200 miles away, at 50 mph. The number of miles, n, that you have left to travel after t hours. Is the relationship a direct variation or not?

Answer 1

Answer:

Not a direct variation

Explanation:

• The distance to the camp = 200 miles

,

• The speed at which you are traveling = 50mph

The number of miles, n, that you have left to travel after t hours can be derived using the formula:

$n=200-50t$

Substitute values of t from 1:

$\begin{gathered} \text{When }t=1,n=200-50(1)=150\text{ miles} \\ \text{When }t=2,n=200-50(2)=100\text{ miles} \\ \text{When }t=3,n=200-50(3)=50\text{ miles} \end{gathered}$

Observe that as the value of t increases, the number of miles, n decreases.

Thus, the relationship between n and t is NOT a direct variation.