Question

Cycing The equation y= 1/8x represents the distance y, in kilometers, that Patrick traveled in x minutes while training for the cycling portion of a triathlon. The table shows the distance y Jennifer traveled in x minutes in her training. Who has the faster training rate? 40 64 80 96 Time (min) Distance (km) 5 8 10 12 Click to add text

Answer 1

The training rate is basically the slope, we can compare the slopes of Patrick and Jennifer to determine whose training rate is faster.

Patrick's slope:

`y=(1)/(9)x`

From the equation, we see that the slope is 1/9 (the coefficient of the variable x is slope)

Jennifer's slope:

We can find the slope for Jennifer by using the given table.

The slope is given by

`m=(y_2-y_1)/(x_2-x_1)`

Where y is the distance (km) and x is the time (mins)

You can select any two x, y pairs from the given table.

Let us select the first two x,y pairs so

`\begin{gathered} (x_1,y_1)=(40,5) \\ (x_2,y_2)=(64,8) \end{gathered}`

Substitute these points into the above slope formula.

`m=(y_2-y_1)/(x_2-x_1)=(8-5)/(64-40)=(3)/(24)=(1)/(8)`

So, the slope for Jennifer's training is 1/8

Comparison:

`\begin{gathered} (1)/(8)>(1)/(9) \\ 0.125>0.111 \end{gathered}`

Since the slope of Jennifer is greater than the slope of Patrick

Therefore, Jennifer has a faster training rate.