Chapter 6.3, Problem 40E

(a)

To determine

The total distance travelled.

Answer to Problem 40E

The total distance travelled is 300 miles.

Explanation of Solution

Given information:

A driver averaged 30 mph on a ISO-mile Hip and then returned over the same 150 miles at the rate of 50 mph. He figured that his average speed wan 40 mph for the entire trip.

Formula used:

The speed will get added up.

Calculation:

Since driver return over the same path. Total distance travelled is given by

  $\begin{array}{l}\text{total distance traveled}=\left(150+150\right)\text{miles}\\ \text{total distance traveled}=300\text{miles}\end{array}$

Conclusion:

The total distance travelled is 300 miles.

(b)

To determine

The total time spent for the trip.

Answer to Problem 40E

The total time spent is 8 hours.

Explanation of Solution

Given information:

A driver averaged 30 mph on a ISO-mile Hip and then returned over the same 150 miles at the rate of 50 mph. He figured that his average speed wan 40 mph for the entire trip.

Formula used:

The ratio of the distance to speed

Calculation:

Time is calculated by ratio of the distance to speed.

  $\begin{array}{l}\text{total time spent}=\frac{150}{30}+\frac{150}{50}\\ =5+3\\ \text{total time spent}=8\text{hours}\end{array}$

Conclusion:

The total time spent is 8 hours.

(c)

To determine

The average speed of the trip.

Answer to Problem 40E

The average speed is 37.5 miles per hour.

Explanation of Solution

Given information:

A driver averaged 30 mph on a ISO-mile Hip and then returned over the same 150 miles at the rate of 50 mph. He figured that his average speed wan 40 mph for the entire trip.

Formula used:

Average speed is given by total distance travelled divided by total time spent.

Calculation:

Average speed is given by total distance travelled divided by total time spent.

  $\begin{array}{l}\text{average speed}=\frac{150}{\frac{150}{30}}+\frac{150}{\frac{150}{50}}\\ =\frac{300}{5+3}\\ =\frac{300}{8}\\ \text{average speed}=37.5\text{miles per hours}\end{array}$

Conclusion:

The average speed is 37.5 miles per hour.

(d)

To determine

The error is the driver’s speed.

Answer to Problem 40E

The neither two expressions are equal nor the two values obtained.

Explanation of Solution

Given information:

A driver averaged 30 mph on a ISO-mile Hip and then returned over the same 150 miles at the rate of 50 mph. He mainly figured that his average speed wan 40 mph for the entire trip.

Formula used:

  $\text{average speed}=\frac{1}{2}\left[\frac{d_1}{t_1}+\frac{d_2}{t_2}\right]$

Calculation:

Driver calculated the average speed by averaging the average speeds for forward journey and backward journey.

d₁ and d_2. These are distance travelled or forward journey and backward journey and t₁ and t₂ are time taken in forward journey and backward journey. Then according to driver,

  $\begin{array}{l}\text{average speed}=\frac{1}{2}\left[\frac{d_1}{t_1}+\frac{d_2}{t_2}\right]\\ =\frac{1}{2}\left[\frac{150}{\frac{150}{30}}+\frac{150}{\frac{150}{50}}\right]\\ =\frac{1}{2}\left[\frac{150}{5}+\frac{150}{3}\right]\\ \text{average speed}=40\text{mph}\end{array}$

But, actual average speed is calculated by

  $\begin{array}{l}\text{average speed}=\left[\frac{d_1}{t_1}+\frac{d_2}{t_2}\right]\\ =\left[\frac{150}{\frac{150}{30}}+\frac{150}{\frac{150}{50}}\right]\\ =\left[\frac{300}{8}\right]\\ \text{average speed}=37.5\end{array}$

You can observe, neither two expressions are equal nor the two values obtained.

Conclusion:

The neither two expressions are equal nor the two values obtained.