Flying against the wind, Lisa made the flight from Reno in 3 h with a steady airspeed of 400km/h. Returning later with a tail wind that had doubled in magnitude, she landed 225 km beyond the starting point in 3 h. What was the original wind speed? How far from Reno did she begin the trip?.........I know how to solve i just need the two equations.
speed upwind =400-w
distance upwind = d = (400-w)(3)
down the breeze:
d+225=(400+2w)(3)
soo the two equations i would use
d = (400-w)(3)
d=(400+2w)(3)-225
soo w= 25km/hr
To solve this problem, we can set up two equations based on the given information.
Let's denote the original wind speed as "w" (in km/h), and the distance from Reno to the starting point as "d" (in km).
First, let's consider Lisa's flight against the wind. The time taken for this leg of the journey is 3 hours, and her airspeed is given as 400 km/h. Since she is flying against the wind, her effective ground speed will be the difference between her airspeed and the wind speed. Therefore, the equation for this leg of the journey is:
d = (400 - w) * 3
Next, let's consider Lisa's return flight with the tailwind. Again, the time taken for this leg of the journey is 3 hours, but this time her airspeed is still 400 km/h since it is not affected by the wind. With the tailwind, her effective ground speed will be the sum of her airspeed and the wind speed. The equation for this leg of the journey is:
d + 225 = (400 + 2w) * 3
Now, you can solve these two equations simultaneously to find the values of "w" and "d".
x = speed of airplane
y = wind speed
With tailwind = 400/3 = 133.3
With headwind = 225/3 = 75
x + y = 133.3
x - y = 75
x + x + y - y = 208.3
2x = 208.3
x = 104.15
104.15 - y = 75
104.15 - 75 = y
29.15 = y
y = 29.15
The natural speed of the aircraft is 104.15km/h while the wind speed is 29.15km/h.