Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. To keep in shape, Tisha exercises at a track near her home. She requires 24 minutes to do 6 laps running and 3 laps walking. In contrast, she requires 20 minutes to do 6 laps running and 2 laps walking. Assuming she maintains a consistent pace while running and while walking, how long does Tisha take to complete a lap? Tisha takes minutes to run a lap and minutes to walk a lap.

Answer 1

Let R be the minutes Tisha runs and W be the minutes Tisha walks. Since she requires 24 minutes to do 6 laps running and 3 laps walking, we have the following equation:

`6R+3W=24`

Now, when she requires 20 minutes to do 6 laps running and 2 laps walking, we have:

`6R+2W=20`

So, we have the following system of equations:

`\mleft\{\begin{aligned}6R+3W=24 \\ 6R+2W=20\end{aligned}\mright.`

We are going to solve it by elimination. Notice that the coefficients of R are the same, so we just have to multiply one equation by -1 and add it altogether to the other equation:

`\begin{gathered} (6R+2W=20)(-1) \\ \Rightarrow-6R-2W=-20 \end{gathered}`

Then:

`\begin{gathered} 6R+3W=24\rbrack \\ -6R-2W=20 \\ \Rightarrow(6R-6R)+(3W-2W)=24-20 \\ \Rightarrow W=4 \end{gathered}`

Now we use the value W=4 to find R:

`\begin{gathered} W=4 \\ 6R+3W=24 \\ \Rightarrow6R+3\cdot4=24 \\ \Rightarrow6R=24-12=12 \\ \Rightarrow6R=12 \\ \Rightarrow R=(12)/(6)=2 \\ R=2 \end{gathered}`

Therefore, it takes Tisha to complete a lap 2 minutes if she's running and 4 minutes if she's walking.