Question

An airplane travels 1200 miles from Annapolis to Dallas in 4.8 hours, going against the wind. The return trip iswith the wind, and takes only 4 hours. Find the rate of the airplane with no wind. Find the rate of the wind.

Answer 1

Answer:

$\begin{gathered} \text{ The rate of the airplane with no wind is 275 mph} \\ \text{ The rate of the wind is 25mph} \end{gathered}$

Step-by-step explanation:

Speed is represented by the relation of the distance and time, therefore for the speed against the wind;

$\begin{gathered} \text{ Speed=}\frac{1200}{4.8} \\ \text{ Speed=}250\text{ miles per hour} \end{gathered}$

Therefore, let x be the wind speed.

let y be the airplane speed at no wind.

$y-x=250\text{ (1)}$

Now, the speed with the wind:

$\frac{1200}{4}=300\text{ miles per hour}$$\begin{gathered} y+x=300\text{ (2)} \\ x=300-y \end{gathered}$

Hence, use the method of substitution to solve the system of equations. Substitute (2) into (1):

$\begin{gathered} y-(300-y)=250 \\ y-300+y=250 \\ 2y=550 \\ y=\frac{550}{2} \\ y=275\text{ mph} \end{gathered}$

Knowing the value of the plane with no wind. Substitute y into (2) to find the speed of the wind:

$\begin{gathered} x=300-275 \\ y=25\text{ mph} \end{gathered}$