D=120 when t=30.find the relationship between d and t

1 answer

To find the relationship between \( d \) (distance) and \( t \) (time) based on the given information \( d = 120 \) when \( t = 30 \), we can assume a linear relationship of the form:

\[ d = kt + b \]

where \( k \) is the slope (rate of change) and \( b \) is the y-intercept.

Given that we have one point \((t, d) = (30, 120)\), we can express \( d \) in the context of \( t \) as follows:

  1. Let's assume \( b = 0 \) for simplicity, which simplifies the equation to \( d = kt \).

  2. From the point \( (30, 120) \), we can solve for \( k \):

\[ 120 = k \cdot 30 \]

Dividing both sides by \( 30 \):

\[ k = \frac{120}{30} = 4 \]

So, if we assume a relationship that passes through the origin:

\[ d = 4t \]

Thus, the relationship between \( d \) and \( t \) can be described as:

\[ d = 4t \]

This means that for every unit increase in \( t \), \( d \) increases by 4 units. If you have further data or want to consider another form (for instance, including a non-zero intercept), please provide that context.