A single engine aircraft can fly 120 mph in still air. If the aircraft can fly 490 miles flying with the wind in the same amount time it can fly 350 miles when flying against the wind, what is the speed of the wind? I can't figure out how to set up the equation.
d = (120+V)T = 490 mi.
Eq1: 120T + VT = 490.
Eq2: 120T - VT = 350.
Sum: 240T = 840.
T = 3.5 h.
In Eq1, replace T with 3.5 and solve for
V.
To solve this problem, you need to set up an equation using the given information. Let's assume the speed of the wind is represented by 'w' in mph.
When the aircraft is flying with the wind, its effective speed is the sum of its airspeed (120 mph) and the speed of the wind (w mph). So, the effective speed is 120 + w mph.
Similarly, when the aircraft is flying against the wind, its effective speed is the difference between its airspeed and the speed of the wind. So, the effective speed is 120 - w mph.
Now, let's consider the time taken to cover a certain distance:
Time = Distance / Speed
When flying with the wind, the time taken to cover 490 miles is given by:
Time with wind = 490 / (120 + w) hours
Similarly, when flying against the wind, the time taken to cover 350 miles is given by:
Time against wind = 350 / (120 - w) hours
It is mentioned in the problem that the time taken for both scenarios is the same. Therefore, we can equate the expressions for time:
490 / (120 + w) = 350 / (120 - w)
To solve this equation for 'w,' we can cross-multiply and simplify:
490(120 - w) = 350(120 + w)
Solving this equation will give you the value of 'w,' which represents the speed of the wind.