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

Answer 1

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.