Flying to the wind, an airplane takes 4 hours to go 960 km. The same plane flying with the wind takes only 3 hours to make the same trip. Find the speed of the plane and the speed of the wind.

I wasn't here for the lesson from my teacher but told me to ask my classmates but there not replying to me. I know distance = speed over time. I tryed using the substituion method but idk i just mess up. Thanks.

You have to consider the speed of the plane without wind and the speed of the wind itself

Let the speed of the plane in still air be x km/h
le the speed of the wind be y km/h

so going with the wind -- speed is x+y mph
going against the wind -- speed is x - y mph

2 equations:
4(x-y) = 960
4x - 4y = 960
x - y = 240 ----- #1

3(x+y) = 960
3x + 3y = 960
x + y = 320 ----#2

these are easy to solve, just add them and after that its simple

To solve this problem, let's use a system of equations.

Let's assume the speed of the plane is represented by "p" (in km/h) and the speed of the wind is represented by "w" (in km/h).

When the airplane is flying against the wind, its effective speed would be reduced by the speed of the wind. Therefore, the equation for this scenario would be:

960 = (p - w) * 4 (Equation 1)

Similarly, when the airplane is flying with the wind, its effective speed would be increased by the speed of the wind. Therefore, the equation for this scenario would be:

960 = (p + w) * 3 (Equation 2)

Now we have a system of equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of "p" and "w".

Let's solve this system using the substitution method:

From Equation 1, we can simplify it to:

240 = p - w (Equation 3)

Let's solve Equation 3 for "p":

p = w + 240 (Equation 4)

Now let's substitute Equation 4 into Equation 2:

960 = (w + 240 + w) * 3

960 = (2w + 240) * 3

Now distribute the 3:

960 = 6w + 720

Rearrange the equation:

6w = 960 - 720

6w = 240

Divide by 6:

w = 40

Now, substitute this value of "w" back into Equation 4 to find "p":

p = 40 + 240

p = 280

Therefore, the speed of the plane is 280 km/h, and the speed of the wind is 40 km/h.

To solve this problem, we can use a system of equations. Let's assume the speed of the plane is x km/h and the speed of the wind is y km/h.

When the airplane flies against the wind, the effective speed will be reduced. So, the equation for this scenario can be written as:
x - y = (960 km)/(4 hours) = 240 km/h

When the airplane flies with the wind, the effective speed will be increased. So, the equation for this scenario can be written as:
x + y = (960 km)/(3 hours) = 320 km/h

Now, we have a system of equations:

Equation 1: x - y = 240
Equation 2: x + y = 320

To solve this system, we can add both equations to eliminate the variable y:

(x - y) + (x + y) = 240 + 320
2x = 560
x = 560/2
x = 280 km/h

Now, we can substitute the value of x into either of the original equations to find the value of y:

x + y = 320
280 + y = 320
y = 320 - 280
y = 40 km/h

Therefore, the speed of the plane is 280 km/h and the speed of the wind is 40 km/h.

Well, well, well, the airplane seems to be having a productive relationship with the wind! Let's solve this together, shall we?

Let's say the speed of the plane is "p" and the speed of the wind is "w".

When flying against the wind, the effective speed of the plane is reduced by the speed of the wind. So the equation for that is:

960 km = (p - w) * 4 hours ---(Equation 1)

When flying with the wind, the effective speed of the plane is increased by the speed of the wind. So the equation for that is:

960 km = (p + w) * 3 hours ---(Equation 2)

Now, let's simplify and solve this conundrum, my friend!

Expanding Equation 1, we get:
960 km = 4p - 4w

Expanding Equation 2, we get:
960 km = 3p + 3w

From here, we can solve this system of equations using the substitution method or by adding the two equations together. Let's go with the substitution method for now!

From Equation 1, we can isolate p:
4p = 960 km + 4w
p = (960 km + 4w)/4

Now, substitute p back into Equation 2:
960 km = 3[(960 km + 4w)/4] + 3w

Alright, let's simplify further!

960 km = 3 * 960 km/4 + 3w + 3w

To make things easier, let's convert the right side of the equation to have a common denominator:

960 km = 3(960 km + 4w)/4 + 6w/4

960 km = 2880 km/4 + 960 w/4 + 6w/4

960 km = 720 km + 960 w + 6w/4

Subtracting 720 km from both sides:

960 km - 720 km = 960 w + 6w/4

240 km = (960 w + 6w)/4

240 km = (966 w)/4

240 km * 4 = 966w

960 km = 966w

Dividing both sides by 966:

960 km/966 = w

Approximately, the speed of the wind is 0.993 km/hr.

Now that we have the speed of the wind, we can substitute it back into either Equation 1 or Equation 2 to find the speed of the plane (p). I'll leave that part to you, my friend! Keep up the good work!