Question

What is the Unit Rate for each cyclist?

Answer 1

Answer:

Cyclist A  12 mi/h

Cyclist B  5 mi/h

Cyclist C  9 mi/h

Cyclist D  10 mi/h

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem the relation between the distance and the time represent a direct variation

Let

y -----> the distance in miles

x ----> the time in hours

The unit rate is the same that the slope or constant of proportionality of the linear equation

Cyclist A

we have

The cyclist can ride 24 miles in 2 hours

The unit rate is equal to divide the total distance by the total time

so

$\frac{24}{2}=12\ \frac{mi}{h}$

Cyclist B

Looking at the table

For x=1 h, y=5 mi

$k=y/x$

substitute

$k=\frac{5}{1}=5\ \frac{mi}{h}$

Cyclist C

we have

$y=9x$

Remember that the unit rate is equal to the slope

so

$m=9\ \frac{mi}{h}$

Cyclist D

Looking at the graph

For x=1 h, y=10 mi

$k=y/x$

substitute

$k=\frac{10}{1}=10\ \frac{mi}{h}$