Question

big ideas math
#6
elizabeth rost
listen
dig deeper a vehicle travels 250 feet every 3 seconds. find the value of the ratio, the unit rate, and the constant of proportionality
the value of the ratio is
the unit rate is feet per second.
the constant of proportionality is
how are they related?

Explanation:

Step1: Find the ratio

The ratio of distance to time is $\frac{250}{3}$.

Step2: Find the unit rate

The unit rate is the distance per second, which is also $\frac{250}{3}\approx83.33$ (but as a fraction, it's $\frac{250}{3}$).

Step3: Find the constant of proportionality

In a proportional relationship $d = kt$ (where $d$ is distance, $t$ is time, and $k$ is the constant of proportionality), $k$ is the ratio of $d$ to $t$, so it's also $\frac{250}{3}$.

For the value of the ratio:

The ratio of distance (250 feet) to time (3 seconds) is $\frac{250}{3}$.

For the unit rate:

The unit rate is $\frac{250}{3}$ feet per 1 second (since unit rate is per 1 unit of time).

For the constant of proportionality:

In the proportional relationship between distance and time, the constant of proportionality is the same as the unit rate and the ratio, so it's $\frac{250}{3}$.

Answer:

s:
The value of the ratio is $\boldsymbol{\frac{250}{3}}$.

The unit rate is $\boldsymbol{\frac{250}{3}}$ feet per $\boldsymbol{1}$ second.

The constant of proportionality is $\boldsymbol{\frac{250}{3}}$.

(Note: If decimal approximation is preferred, $\frac{250}{3}\approx83.33$, but the fractional form is exact.)