Chapter 2, Problem 7P

(a)

To determine

The distance of home town from school.

Answer to Problem 7P

The distance is S = 258.05 km.

Explanation of Solution

Given:

The car runs at a speed of 95 km/h for a distance of 130 km.

For the remaining distance, the speed of the car is 65 km/h. And the total time of the journey is 3 hours 20 min.

Formula used:

Speed (v) , time (t) and distance s is related as,

  $s=vt$

Calculation:

Time required to travel the distance 130 km, is

  $t_1=\frac{S_1}{v_1}=\frac{130}{95}\approx 1.37\text{h}$

Also, total time is $T =3\text{ h }20\text{ min}\approx 3.34\text{h}$ .

So the remaining time is

  $\begin{array}{c}{t}_2=(3.34-1.37)\text{h}\\ \text{=1}\text{.97}\text{h}\end{array}$

During this time, car travelled with a speed of $v_2=65$ km/h.

So, the distance travelled at time $t_2$ is $S_2=v_2{t}_2=(65\times 1.97)$ km = 128.05 km.

The total distance is $S=S_1+S_2=(130+128.05)$ km. = 258.05 km.

Conclusion:

Therefore, the distance of home town from school is S = 258.05 km

(b)

To determine

The average speed of the car.

Answer to Problem 7P

The average speed of the car is 77.26 km/h.

Explanation of Solution

Given:

The car runs at a speed of 95 km/h for a distance of 130 km. For the remaining distance, the speed of the car is 65 km/h. And the total time of the journey is 3 hours 20 min.

Formula used:

Average speed of the car is the total distance travelled by the car divided by the total time for its whole journey.

Calculation:

Here total time is $T=3.34\text{h}$ and total distance is S = 258.05 km.

So average speed is $\overline{v}=\frac{S}{T}=\frac{258.05}{3.34}\text{km/h}=77.26\text{ km/h}$

Conclusion:

Therefore, average speed of the car is 77.26 km/h.