janekelly said:
I need help setting up the equations so I can solve it.
A plane traveled 576 miles to Chicago and back. The trip there was with the wind. It took 6 hours. The trip back was into the wind. The trip back took 12 hours. What is the speed of the plane in still air? What is the speed of the wind?
I've never known the winds aloft to blow that steadily, either in speed or direction, for that length of time, but assuming a first time for everything:
(I'm assuming that you mean the trip to Chicago was 576 miles, and the trip back was also 576 miles.)
Remember that the distance is the product of the rate (speed) and time, i.e., d = rt.
Let "a" be the speed of the plane when traveling with the wind, and "b" be the speed of the plane when traveling against the wind. For the trip with the wind, we're given that:
576 = a(6)
a = 576/6 = 96 miles/hr
For the trip against the wind, we're given that:
576 = a(6)
b = 576/12 = 48 miles/hr
Assuming the speed of the plane in still air is "r,", the speeds are related:
a - r = b + r
2r = a - b
r = (a - b)/2 = (96 + 48)/2 = 72 miles/hr (plane speed)
w = a - r = b + r = 24 miles/hr (windspeed)
