Chapter 5.4, Problem 14Q

a.

To determine

To calculate:The time spends on driving at each speed on highways and on the rest of the roads.

Answer to Problem 14Q

1 hour is spent driving on the highways and 2 hours are spent driving on the rest of the roads.

Explanation of Solution

Given information:It takes 3 hours to drive to a concert 135 miles away. On the highways the speed is 55 miles per hour and on the rest of the road the speed is 40 miles per hour.

Calculation:Let time taken on the highways be x hours and that on rest of the roads be y hours.

Speed on the highways $=$ 55 miles per hour

Then, distance travelled on the highway $=55x$ miles

Speed on the rest of the roads $=$ 40 miles per hour

Then, distance travelled on the highway $=40x$ miles

According to the problem, total time taken is 3 hours and total distance travelled is 135 miles.

Then,

  $\begin{array}{l}x+y=\mathrm{3........................}(1)\\ 55x+40y=\mathrm{135............}(2)\end{array}$

From equation (1),

  $\begin{array}{l}x+y=3\\ \Rightarrow y=3-x\mathrm{...................}(3)\end{array}$

Putting (3) in (2),

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

Putting $x=1$ in (3),

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

Thus, time taken highways is 1 hour and time taken on the rest of the road is 2 hours.

b.

To determine

To calculate:Distance driven on highways and on rest of the roads.

Answer to Problem 14Q

55 miles are driven on the highways and 80 miles are driven on the rest of the roads.

Explanation of Solution

Given information:It takes 3 hours to drive to a concert 135 miles away. On the highways the speed is 55 miles per hour and on the rest of the road the speed is 40 miles per hour.

Calculation:Speed on the highways $=$ 55 miles per hour.

Time taken on highways $=1$ hour

Then, total distance travelled on highways $=55\times 1=55$ miles

Speed on the rest of the roads $=$ 40 miles per hour.

Time taken on rest of the roads $=2$ hour

Then, total distance travelled on rest of the roads $=40\times 2=80$ miles.

Thus, 55 miles are driven on the highways and 80 miles are driven on the rest of the roads.