Chapter 3.5, Problem 46E

a.

To determine

To write and solve an inequality to find the average speeds at which caribou can migrate.

Answer to Problem 46E

The inequality to find the average speeds at which caribou can migrate is $x\le \frac{36}{24}$ and the average speed of caribou must be less than or equal to 1.5 miles per hour.

Explanation of Solution

Given information:

A herd of caribou can migrate as far as 36 miles in 24 hours.

Formula used:

Average speed is defined by:

  $\text{Average Speed}=\frac{\text{Distance}}{\text{Time}}$

Calculation:

Maximum distance which the herd can migrate in 24 hours is 36 miles.

Let, $x$ miles per hour be the average speed of the herd.

So, distance covered by the herd in 24 hours is obtained as:

  $\text{Average speed}\times \text{Time}=x\times 24$

Since, the distance at which the caribou can migrate must be less than or equal to 36 miles.

Hence, the inequality is obtained as:

  $\begin{array}{l}x\times 24\le 36\\ \frac{x\times 24}{24}\le \frac{36}{24}\text{ [Divide each sides by 24]}\\ x\le 1.5\text{ [Simplify]}\end{array}$

Hence, the average speed of caribou must be less than or equal to 1.5 miles per hour

b.

To determine

To graph the distance (in miles) the herd could have travelled.

Explanation of Solution

Given information:

A herd of caribou can migrate as far as 36 miles in 24 hours.

Graph:

The caribou herd has been moving for three days.

Number of hours in one day is 24 hours.

So, number hours in three days is $24\times 3=108$ hours.

Let, $x$ be the distance travelled by the caribou in three days.

So, the equation is obtained as:

  $\begin{array}{l}\frac{36}{24}=\frac{x}{108}\\ 24x=36\times 108\text{ [Cross multiply]}\\ \frac{24x}{24}=\frac{3888}{24}\text{ [Divide each sides by 24]}\\ x=162\end{array}$

The distance travelled by the caribou in three days is 162 miles.

The graph of the distance (in miles) the herd could have travelled in 3 days is shown below: