Chapter 8.6, Problem 20PPSE

Solution

a.

To identify:The time for the trip. A plane flies 700 miles from new York to Chicago at a speed of $360\text{mi/h}$ .

The speed of an airplane is given by $s=\frac{d}{t}$ , where $d$ represents the distance and $t$ is the time.

The time required to travel a distance is $t\approx 1.9\text{hour}$

Given information:

A plane travels from new york to chicago at a speed of $s=360\text{mi/h}$ .

Distance traveled by the flight is $d=700$ miles.

Explanation:

Consider the given information

A plane travels from new york to chicago at a speed of $s=360\text{mi/h}$ .

Distance traveled by the flight is $d=700$ miles.

Put the value of $dands$ into $s=\frac{d}{t}$

  $\begin{array}{c}360=\frac{700}{t}\\ t=\frac{700}{360}\\ t=\frac{35}{18}\\ t\approx 1.9\text{hour}\end{array}$

Hence the time required to travel a distance is $t\approx 1.9\text{hour}$

b.

To identify:The speed $x$ of the tail wind. On the return trip from Chicago to New York, a tail wind helps the plane move faster. The total flying time for the round trip is $3.5\text{h}$

The speed of an airplane is given by $s=\frac{d}{t}$ , where $d$ represents the distance and $t$ is the

time.

.The speed of the tail wind is $100\text{mi/h}$

Given information:

The total flying time for the round trip is $3.5\text{h}$

Explanation:

Consider the given information.

Let $x$ is the speed of the tail wind.

Then the speed of the flight is $s=x+350\text{mi/h}$ .

Time required to travel a return trip is

  $\begin{array}{c}t=\frac{d}{s}\\ t=\frac{700}{x+350}\end{array}$

Total time taken for a round trip is

  $\frac{35}{18}+\frac{700}{x+350}=3.5\mathrm{....}\left(2\right)$

Now solve the rational equation (2).

Multiply the equation on both sides by $18\left(x+350\right)$

  $\begin{array}{c}\left(\frac{35}{18}+\frac{700}{x+350}\right)18\left(x+350\right)=3.5\times 18\left(x+350\right)\\ 35\left(x+350\right)+700\times 18=63x+22050\\ 35x+12250+12600=63x+22050\\ 2800=28x\\ x=100\end{array}$

Hence the speed of the tail wind is $100\text{mi/h}$