Flying against the wind, an airplane travels 5600 km in 8 hours. Flying with the wind, the same plane travels 9900 km in 9 hours.
speed of plane without wind ---- x km/h
speed of wind --------- y km/n
5600/(x-y) = 8
700/(x-y) = 1
x-y = 700 **
9900/(x+y) = 9
1100/(x-y) = 1
x + y = 1100 ***
add ** and *** to find x
then sub back into **
To find the speed of the airplane and the speed of the wind, we can set up a system of equations:
Let's assume the speed of the airplane is represented by 'a' (in km/h) and the speed of the wind is represented by 'w' (in km/h).
When flying against the wind:
5600 = (a - w) * 8 -- Equation 1
When flying with the wind:
9900 = (a + w) * 9 -- Equation 2
Now, we will solve the system of equations to find the values of 'a' and 'w'.
First, let's simplify Equation 1:
5600 = 8a - 8w
Next, let's simplify Equation 2:
9900 = 9a + 9w
Now we can rearrange Equation 1 to solve for 'a' in terms of 'w':
8a = 5600 + 8w
a = (5600 + 8w)/8
Substituting this value of 'a' into Equation 2, we get:
9900 = 9[(5600 + 8w)/8] + 9w
Simplifying further:
9900 = (6300 + 9w) + 9w
9900 = 6300 + 18w
18w = 9900 - 6300
18w = 3600
w = 200
Now that we have the value of 'w', we can substitute it back into Equation 1 to find 'a':
5600 = (a - 200) * 8
5600 = 8a - 1600
8a = 7200
a = 900
Therefore, the speed of the airplane is 900 km/h and the speed of the wind is 200 km/h.
To find the speed of the airplane and the speed of the wind, we can use the formula:
Speed of the airplane against the wind = (Distance traveled against the wind) / (Time taken against the wind)
Speed of the airplane with the wind = (Distance traveled with the wind) / (Time taken with the wind)
Let's start with the speed of the airplane against the wind:
Speed against the wind = 5600 km / 8 hours = 700 km/h
Now, let's find the speed of the airplane with the wind:
Speed with the wind = 9900 km / 9 hours = 1100 km/h
To find the speed of the wind, we need to subtract the speed of the airplane against the wind from the speed of the airplane with the wind:
Speed of the wind = Speed with the wind - Speed against the wind
Speed of the wind = 1100 km/h - 700 km/h = 400 km/h
So, the speed of the airplane is 700 km/h and the speed of the wind is 400 km/h.