An airplane makes a 400-mile trip against a head wind in 4 hours. the return trip takes 2.5 hours, the wind now being a tall wind. if the plane maintains a constant speed with respect to still air, and the speed of the wind is also constant and does not vary, find the still-air speed of the plane and the speed of the wind.

Step-by-step explanation:

Lets call the the still-air speed of the plane and the speed of the wind. On the first part the speed of the plane relative to the ground will be , and on the second part it will be .

We know that the distance d=400 miles on the first and second parts are the same, so by the definition of velocity we will have:

Or:

Adding both equations:

Which for our values is:

If instead of adding, we substact, we would have:

Which for our values is:

y = (1/2)x + 5/2

Step-by-step explanation:

y - 3 = (1/2)(x - 1) is in point-slope form.  To obtain the slope-intercept equivalent, solve this equation for y:

y = 3 + (1/2)x - 1/2, or

y = (1/2)x + 3 - 1/2, or

y = (1/2)x + 5/2