Question

It takes Max 5.5 minutes to do 60 pullups which includes a break in between. It takes him 8

Answer 1

Using the given information, we have the points (5.5, 60) and (8, 150). Let's find the ratio-

$r=\frac{y_2-y_1}{x_2-x_1}$

Where

$\begin{gathered} x_1=5.5 \\ x_2=8 \\ y_1=60 \\ y_2=150 \end{gathered}$$\begin{gathered} r=\frac{150-60}{8-5.5}=\frac{90}{2.5} \\ r=36 \end{gathered}$

This ratio represents the slope of the linear equation.

Then, we use the point-slope formula to find the equation that models this situation

$\begin{gathered} y-y_1=m(x-x_1) \\ y-60=36(x-5.5) \\ y=36x-198+60 \\ y=36x-138 \end{gathered}$

The correct equation is the third option.

Now, we can find the number of pulls after 30 minutes using the equation

$y=36\cdot30-138=942$

The number of pull-ups after 30 minutes is 942.