Chapter 6.4, Problem 18P

A plane leaves Chicago and flies 750 miles to New York. It it takes 2.5 hours to get to New York flying against the wind, but only 2 hours to fly back to Chicago, what is the plane’s rate of speed and what is the wind speed?

To determine

To find the plane’s rate of speed and the wind speed

Answer to Problem 18P

Speed of plane is 337.5 miles per hour

Speed of wind is 37.5 miles per hour

Explanation of Solution

Given:

Distance between Chicago and New York is 750 miles

Formula Used:

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

Calculation:

Let,

The speed of the plane be $x$ miles per hour

The speed of wind be $y$ miles per hour

Now, the net speed of plane while going from Chicago to New York while flying against the wind is $(x-y)$ miles per hour.

And, the net speed of plane while going from New York to Chicago while flying along the wind is $(x+y)$ miles per hour.

Since, it takes $2.5$ hours to fly from Chicago to New York, therefore,

  $\Rightarrow x-y=\frac{750}{2.5}$

  $\Rightarrow x-y=300$

Also, it takes 2 hours to fly from New York to Chicago, therefore,

$\Rightarrow x+y=\frac{750}{2}$

  $\Rightarrow x+y=375$

Let,

$x-y=300--------(i)$

  $x+y=375-------(ii)$

Now, adding equation ( i ) and ( ii ),

$\begin{array}{l}\Rightarrow (x-y)+(x+y)=300+375\\ \Rightarrow 2x=675\\ \Rightarrow x=\frac{675}{2}\\ \Rightarrow x=337.5\end{array}$

Substituting the value of $x$ in equation ( i ),

  $\begin{array}{l}\Rightarrow 337.5-y=300\\ \Rightarrow y=37.5\end{array}$

Conclusion:

Hence, the speed of plane is 337.5 miles per hour and speed of wind is 37.5 miles per hour.