Question

What is the Unit Rate for each cyclist?

How did you find it?

Be sure to include ALL 4 Cyclists.

Sample Answer: Cyclist A's Unit rate is_______. I found the unit rate by_________

Answer 1

Cyclist A 12 mi/h

Cyclist B 5 mi/h

Cyclist C 9 mi/h

Cyclist D 10 mi/h

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

`(24)/(2)=12\ (mi)/(h)`

Cyclist B

Looking at the table

For x=1 h, y=5 mi

`k=y/x`

substitute

`k=(5)/(1)=5\ (mi)/(h)`

Cyclist C

we have

`y=9x`

Remember that the unit rate is equal to the slope

so

`m=9\ (mi)/(h)`

Cyclist D

Looking at the graph

For x=1 h, y=10 mi

`k=y/x`

substitute

`k=(10)/(1)=10\ (mi)/(h)`