A certain aircraft can fly 768 miles with the wind in 4 hours and travel the same distance against the wind in 6 hours. what is the speed of the wind?

speed of the plane without wind --- x mph

speed of the wind ---- y mph

time with wind :
4(x+y) = 768
x + y = 192

time against wind:
6(x-y) = 768
x-y = 128

add them
2x = 320
x = 160
then 160+y = 192
= 32

windspeed = 32 mph

check: speed with wind = 160+32 = 192 mph
time to go 768 = 768/192 = 4
speed against wind = 160-32 = 128
time against wind = 768/128 = 6

To find the speed of the wind, we can use the formula:

Speed of aircraft with the wind = Distance / Time

and

Speed of aircraft against the wind = Distance / Time

Let's assume the speed of the aircraft is A and the speed of the wind is W.

Given that the aircraft can fly 768 miles with the wind in 4 hours, we can write the equation as:

A + W = 768 / 4

Similarly, the aircraft can travel the same distance against the wind in 6 hours, so the equation becomes:

A - W = 768 / 6

Now we have a system of two equations:

A + W = 192 ...(Equation 1)
A - W = 128 ...(Equation 2)

To solve these equations, we can add them together:

(A + W) + (A - W) = 192 + 128

This simplifies to:

2A = 320

Now, we can solve for A by dividing both sides by 2:

A = 320 / 2

A = 160

So, the speed of the aircraft is 160 mph.

To find the speed of the wind, we can substitute the value of A into either Equation 1 or Equation 2. Let's use Equation 1:

160 + W = 192

Subtracting 160 from both sides gives:

W = 192 - 160

W = 32

Therefore, the speed of the wind is 32 mph.

To find the speed of the wind, we can use the formula:

Speed of aircraft with the wind = (speed of aircraft + speed of wind)
Speed of aircraft against the wind = (speed of aircraft - speed of wind)

Given that the aircraft can fly 768 miles with the wind in 4 hours:

Speed of aircraft with the wind = 768 miles / 4 hours = 192 mph

And the aircraft can travel the same distance against the wind in 6 hours:

Speed of aircraft against the wind = 768 miles / 6 hours = 128 mph

Now, we have two equations:

192 = speed of aircraft + speed of wind
128 = speed of aircraft - speed of wind

We can solve these equations to find the speed of the wind.

Adding the two equations gives:

192 + 128 = speed of aircraft + speed of wind + speed of aircraft - speed of wind
320 = 2 * speed of aircraft
speed of aircraft = 320 / 2
speed of aircraft = 160 mph

Substituting the value of speed of aircraft into one of the equations:

128 = 160 - speed of wind
speed of wind = 160 - 128
speed of wind = 32 mph

Therefore, the speed of the wind is 32 mph.