A small plane flying into the wind takes 3h 20 min to complete a flight of 960 km.Flying with the wind, the same plane takes 2h 30 min to make the trip. What is the speed of the plane? What is the speed of the wind?
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To find the speed of the plane and the speed of the wind, we can use a system of equations. Let's denote the speed of the plane as P and the speed of the wind as W.
1. When flying into the wind:
The total time taken to complete the flight is 3 hours and 20 minutes, which is equivalent to 3 + 20/60 = 3.33 hours.
The distance covered is 960 km.
Since the plane is flying into the wind, it faces a relative speed of P - W (plane speed minus wind speed).
Therefore, the equation representing this situation can be written as:
960 = (P - W) * 3.33
2. When flying with the wind:
The total time taken to complete the flight is 2 hours and 30 minutes, which is equivalent to 2 + 30/60 = 2.5 hours.
Again, the distance covered is 960 km.
Since the plane is flying with the wind, it experiences a relative speed of P + W (plane speed plus wind speed).
Hence, the equation representing this situation can be written as:
960 = (P + W) * 2.5
To solve this system of equations, we can use the method of substitution. Let's solve the first equation for P:
960 = (P - W) * 3.33
960/3.33 = P - W
288.29 + W = P
Now substitute this value of P in the second equation:
960 = (288.29 + W + W) * 2.5
960 = (288.29 + 2W) * 2.5
960 = 720.725 + 5W
960 - 720.725 = 5W
239.275 = 5W
W = 239.275/5
W = 47.855 km/h
Now that we have the value of W, we can substitute it back into the first equation to find P:
288.29 + W = P
288.29 + 47.855 = P
336.145 = P
Therefore, the speed of the plane (P) is 336.145 km/h, and the speed of the wind (W) is 47.855 km/h.