a small plane flying into the wind takes 3 hrs 20 min to complete a flight of 960 km. Flying with the wind the same plane takes 2 h 30 min to make the trip.what is the speed of the plane? what is the speed of the wind?
To find the speed of the plane and the speed of the wind, we can set up a system of equations based on the given information.
Let's assume the speed of the plane is represented by the variable "p" (in km/h) and the speed of the wind is represented by the variable "w" (in km/h).
When the plane flies into the wind, its effective speed (relative to the ground) is reduced by the speed of the wind. Therefore, the equation representing the time taken to complete the flight into the wind is:
960 km = (p - w) * (3 hours + 20 minutes) = (p - w) * 3.33 hours
Similarly, when the plane flies with the wind, its effective speed (relative to the ground) is increased by the speed of the wind. Therefore, the equation representing the time taken to complete the flight with the wind is:
960 km = (p + w) * (2 hours + 30 minutes) = (p + w) * 2.5 hours
Now, we have a system of two equations:
1) 960 = (p - w) * 3.33
2) 960 = (p + w) * 2.5
To solve this system, we can use the method of substitution or elimination. Let's use the method of elimination:
Multiply equation 1) by 2.5 and equation 2) by 3.33 to eliminate the decimal coefficients:
2.5 * 960 = (p - w) * (3.33 * 2.5)
3.33 * 960 = (p + w) * (2.5 * 3.33)
Simplifying these equations, we get:
2400 = 8.325p - 8.325w
3196.8 = 8.325p + 8.325w
Adding these equations together eliminates the variable "w":
2400 + 3196.8 = 8.325p - 8.325w + 8.325p + 8.325w
5596.8 = 16.65p
Divide both sides by 16.65:
p = 5596.8 / 16.65
Calculating this, we find that the speed of the plane is approximately 336.58 km/h.
To find the speed of the wind, we can substitute the value of p back into one of the original equations, let's use equation 1):
960 = (336.58 - w) * 3.33
Solve for w by rearranging the equation:
w = 336.58 - 960 / 3.33
w = 336.58 - 288.29
Calculating this, we find that the speed of the wind is approximately 48.29 km/h.
So, the speed of the plane is approximately 336.58 km/h and the speed of the wind is approximately 48.29 km/h.
w=speed of wind
a=speed of airplane
Use speed*time = distance
(a-w)*(10/3)=960 ...(1)
(a+2)*(5/2)=960 ...(2)
Solve for a and w.