Question

this is my problem I don't know how to do that help.. please help

Answer 1

We know that Jennifer runs by

$8t+2$

and that Erika can run like

$4t+3$

Erika claims that she runs half what Jennifer can plus 2. Our job is to find out if her claim is correct.

To do that we would like to compare some distances with different values of t. The ones given in the table are:

$\begin{gathered} \begin{bmatrix}{t} & {J} & {E} \\ {1} & {8(1)+2=10} & {4(1)+3=7} \\ {3} & {8(3)+2=26} & {4(3)+3=15}\end{bmatrix} \\ \begin{bmatrix}{5} & {8(5)+2=42} & {4(5)+3=23} \\ {10} & {8(10)+2=82} & {4(10)+3=43} \\ {\square} & {\square} & {\square}\end{bmatrix} \end{gathered}$

Now that we have the values of the table we see in each row if erika's claim is correct. Let's check the first one. If the time is 1 Jennifer runs 10 feet and Erika runs 7. We see that Erika runs half what Jennifer did plus 2; so in this case Erika's claim is correct

Doing the same thing in each row we sse that Erika's claim is correct. But theres another way to do it without the table. Once again, Erika claims that she runs half what Jennifer does plus two, in mathematical terms this means

$\frac{8t+2}{2}+2$

Simplifying this expression we get

$\begin{gathered} \frac{8t+2}{2}+2=\frac{8t}{2}+\frac{2}{2}+2 \\ =4t+1+2 \\ =4t+3 \end{gathered}$

But the last expression is exactly what Erika runs, therefore Erika's claim is true,