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.