Chapter 5.4, Problem 14Q

a)

To determine

To find: The time do you spend driving at each speed.

Answer to Problem 14Q

The time spent on $55mph$ and $40mph$ are $1hr$ and $2hr$ respectively.

Explanation of Solution

Given information: The required time for travelling $135miles$ is $3hr$ . When your speed is $55mph$ and $40mph$ .

Formula used: $\text{distance}=speed\times time$

Let the time spent on $55mph$ is x and y is the spent time on $40mph$ .

Since, total time is $3hr$ ,

  $x+y=3\mathrm{...}\left(1\right)$

And total distance is $135miles$ ,

  $55x+40y=135\mathrm{...}\left(2\right)$

Apply the substitution method,

  $\begin{array}{l}x+y=3\\ \therefore y=3-x\end{array}$

Substitute $y=3-x$ in equation (2),

  $\begin{array}{l}55x+40y=135\\ 55x+40\left(3-x\right)=135\\ 55x-40x+120=135\\ 15x=135-120\\ x=\frac{15}{15}\\ x=1\end{array}$

Substitute $x=1$ in $y=3-x$ ,

  $\begin{array}{l}y=3-1\\ y=2\end{array}$

Therefore, the time spent on $55mph$ and $40mph$ are $1hr$ and $2hr$ respectively.

b)

To determine

To find: The distance you drive on the highways and on the other roads.

Answer to Problem 14Q

The distance you drive on the highways and on the rest of the roads are $55miles$ and $80miles$ respectively.

Explanation of Solution

Given information: The required time for travelling $135miles$ is $3hr$ . When your speed is $55mph$ and $40mph$ .

Formula used: $\text{distance}=speed\times time$

Let the time spent on $55mph$ is x and y is the spent time on $40mph$ .

Since, total time is $3hr$ ,

  $x+y=3\mathrm{...}\left(1\right)$

And total distance is $135miles$ ,

  $55x+40y=135\mathrm{...}\left(2\right)$

Apply the substitution method,

  $\begin{array}{l}x+y=3\\ \therefore y=3-x\end{array}$

Substitute $y=3-x$ in equation (2),

  $\begin{array}{l}55x+40y=135\\ 55x+40\left(3-x\right)=135\\ 55x-40x+120=135\\ 15x=135-120\\ x=\frac{15}{15}\\ x=1\end{array}$

Substitute $x=1$ in $y=3-x$ ,

  $\begin{array}{l}y=3-1\\ y=2\end{array}$

Use equation (2), and substitute $x=1$ in it,

  $\begin{array}{l}d=55x\\ d=55\times 1\\ d=55miles\end{array}$

Use equation (2), and substitute $y=2$ in it,

  $\begin{array}{l}d=40y\\ d=40\times 2\\ d=80miles\end{array}$

Therefore, the distance you drive on the highways and on the rest of the roads are $55miles$ and $80miles$ respectively.