Matt and anna killian are frequent fliers on fast-n-go airlines. they often fly between two cities that are a distance of 1680 miles apart. on one particular trip, they flew into the wind and the trip took 4 hours. the return trip with the wind behind them, only took about 3.5 hours. find the speed of the wind and the speed of the plane in still air.

Wind speed = 30 miles/hour

Plane speed = 450 miles/hour

Step-by-step explanation:

First we have to know the formula for finding speed, which is distance divided by time

Speed = distance/time

Then we label the speed of the plane to be x

And the spend of the wind to be y

From the question, we are told that when the plane flies into the wind, it takes 4 hours to travel a distance of 1680 so we have the time and distance

And since the plane is flying against the wind speed

We can form an equation

x - y = 1680/4

x - y = 420 (1)

Then when the plane is coming back, the wind is going in the same direction with the plane and it take 3.5 hours to cover the same 1680 miles distance, so we form another equation

x + y = 1680/3.5

x + y = 480 (2)

So we solve (1) and (2) simultaneously

x - y = 420 (1)

x + y = 480 (2)

Using elimination method, we eliminate y by adding both equations

2x = 900

x = 450 miles/hour

So therefore, plane speed is 450 miles/hour

Putting the answer in either (1) or (2) to get y

I choose to put it in (2)

x + y = 480

450 + y = 480

y = 480 - 450

y = 30 miles/hour

So therefore, wind speed = 30miles/hour