Question

Please help me solve C. And D. On my algebra homework question 3

Answer 1

We have to set a system of equations to find the running speed (x) and biking speed (y).

From the first sentence, we can write the the distance covered (27 miles) is equal to the distance covered running (time times speed, 2*x) plus the distance biking (1*y):

`2x+y=27`

This is the first equation of the system.

We also have a linear relationship between x and y, that can be deducted from the table:

`y=-(1)/(2)x+18`

We can rearrange this second equation as:

`\begin{gathered} y=-(1)/(2)x+18 \\ 2y=-2\cdot(1)/(2)x+2\cdot18 \\ 2y=-x+36 \\ x+2y=36 \end{gathered}`

Now, we have the system:

`\begin{cases}2x+y=27 \\ x+2y=36\end{cases}`

From the first equation we have that:

`\begin{gathered} 2x+y=27 \\ y=27-2x \end{gathered}`

We can replace y in the second equation and solve for x (substitution method) as:

`\begin{gathered} x+2y=36 \\ x+2(27-2x)=36 \\ x+54-4x=36 \\ -3x=36-54 \\ -3x=-18 \\ x=(18)/(3) \\ x=6 \end{gathered}`

Knowing x, we can calculate y as:

`\begin{gathered} y=27-2x \\ y=27-2\cdot6 \\ y=27-12 \\ y=15 \end{gathered}`

Answer:

c) The running speed (x) is 6 miles/hour.

d) The biking speed (y) is 15 miles/hour.