Chapter 12, Problem 84CLR

To determine

To find: The speed of the plane relative to the ground.

Answer to Problem 84CLR

The speed of the plane relative to the ground $500\text{mph}$ and with air is $500\text{mph}$ .

Explanation of Solution

Given:

The distance travelled is $3000\text{mi}$ .

The increase in speed is of $100\text{mi}/\text{h}$ .

The increase in speed reduces the journey by $1\text{hr}$ .

Calculation:

Consider the speed of the plane in still air is $x$ mile per hour. Then the speed with the tail wind is,

  $x+100\text{mph}$

The time taken by the plane to cover the distance when there is no wind is,

  $\frac{3000}{x}$

The time taken for the journey with the tail wind is,

  $\frac{3000}{x+100}$

Consider increase in speed reduces the journey by $1\text{hr}$ .

  $\begin{array}{l}\frac{3000}{x}-\frac{3000}{x+100}=1\\ x^2+300000-3000x=x^2+100x\\ \left(x+600\right)\left(x-500\right)=0\\ x=500\text{mph}\end{array}$

Then, the speed with the tail wind is $600\text{mph}$ .

Thus, the speed of the plane relative to the ground $500\text{mph}$ and with air is $500\text{mph}$ .