Final answer:
The air speed of the planes is 547.5 mi/h, while the wind speed is 27.5 mi/h. This was determined by setting up two equations using the provided ground speeds and solving for the unknowns.
Step-by-step explanation:
The problem provided is one of relative motion, specifically a type of vector addition problem, commonly encountered in introductory physics. Given are the ground speeds of two airplanes flying in opposite directions between Boston, Massachusetts, and Phoenix, Arizona, with different ground speeds due to the wind's effect. The key to solving this problem is understanding that the airspeed (velocity of the plane through the air) is the same for both planes, and the wind speed (velocity of the wind relative to the ground) affects both planes, adding to one and subtracting from the other.
Let the airspeed of the airplanes be V, and the wind speed be W. For the traveler flying from Boston to Phoenix, the ground speed is V - W = 520 mi/h. For the traveler flying from Phoenix to Boston, the ground speed is V + W = 575 mi/h. We can set up and solve the two equations to find both V (airspeed) and W (wind speed).
- V - W = 520
- V + W = 575
Adding the two equations together eliminates W:
2V = 1095, solving for V gives us the airspeed V = 547.5 mi/h. To find the wind speed W, we can now subtract the first equation from the second:
2W = 575 - 520
W = 55/2
W = 27.5 mi/h
The air speed of the planes is 547.5 mi/h, and the wind speed affecting them is 27.5 mi/h.