In a storm, a plane flew against the wind and took 9 hours to cover 3,600 miles. The return trip, traveling with the wind, took 1 hour less. find the air speed of the plane, and the speed of the wind.

Question

In a storm, a plane flew against the wind and took 9 hours to cover 3,600 miles. The return trip, traveling with the wind, took 1 hour less. find the air speed of the plane, and the speed of the wind.

Answer 1

Speed of plane --- x mph

speed of wind ---- y mph

9(x-y) = 3600
x-y = 400

8(x+y) = 3600
x+y = 450

add them:
2x = 850
x = 425 , and y = 25

Answer 2

To solve this problem, we need to set up two equations based on the given information and then solve for the unknowns, which are the plane's airspeed and the wind speed.

Let's say the plane's airspeed is represented by "p" (in miles per hour) and the wind speed is represented by "w" (in miles per hour). Then we can establish the following equations:

Equation 1: Time taken against the wind = 9 hours
Equation 2: Time taken with the wind = 9 - 1 = 8 hours (since the return trip took 1 hour less)

Now, let's determine the distances traveled in each trip.

Against the wind, the plane's speed relative to the ground would be its airspeed minus the wind speed, so the distance covered would be (p - w) multiplied by 9.

With the wind, the plane's speed relative to the ground would be its airspeed plus the wind speed, so the distance covered would be (p + w) multiplied by 8.

Given that the distance covered in both cases is equal to 3,600 miles, we can create the following equations:

Equation 3: (p - w) * 9 = 3,600
Equation 4: (p + w) * 8 = 3,600

Now we have a system of two equations with two unknowns (p and w). We can solve this system of equations to find the values of p and w.

Let's solve it step by step:

Step 1: Expand Equation 3 and rewrite it:
9p - 9w = 3,600 ---> p - w = 400 (Dividing both sides by 9)

Step 2: Expand Equation 4 and rewrite it:
8p + 8w = 3,600 ---> p + w = 450 (Dividing both sides by 8)

Now we have a system of two equations with two unknowns:

Equation 5: p - w = 400
Equation 6: p + w = 450

We can solve this system of equations using the method of elimination.

Adding Equation 5 and Equation 6:

(p - w) + (p + w) = 400 + 450
2p = 850

Dividing both sides by 2:
p = 425

Now that we know p (the plane's airspeed), we can substitute it into Equation 5 to find w (the wind speed):

425 - w = 400

Subtracting 425 from both sides:
-w = -25

Multiplying both sides by -1:
w = 25

Therefore, the airspeed of the plane is 425 miles per hour, and the speed of the wind is 25 miles per hour.