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

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

Explanation:

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

`\begin{gathered} \text{ Speed=}(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:

`(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=(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}`