a small plane can fly 1575 miles in 7 hrs in a tailwind. On the return in a headwind, the same trip takes 9 hrs. find the speed in still air (no wind). Then the speed in wind.
speed of plane in still air ---- x mph
speed of wind ------------ y mph
1575/(x+y) = 7
7x+7y = 1575
x+y = 225
1575(x-y) = 9
9x - 9y = 1575
x - y = 175
add them:
2x = 400
x = 200
back-sub:
200+y = 225
y = 25
state your conclusion
To find the speed of the plane in still air, we can start by using the concept of relative speed. Let's call the speed of the plane in still air "S" (in miles per hour) and the speed of the wind "W" (in miles per hour).
In the first case, when there is a tailwind, the plane is flying with the wind. The effective speed of the plane is the sum of its speed in still air and the speed of the wind. So, we have:
Effective speed (with tailwind) = S + W
Given that the plane can fly 1575 miles in 7 hours, we can set up an equation:
(S + W) * 7 = 1575
Next, let's consider the second case, when there is a headwind. The effective speed of the plane is the difference between its speed in still air and the speed of the wind. So, we have:
Effective speed (with headwind) = S - W
Given that the same trip takes 9 hours in a headwind, we can set up another equation:
(S - W) * 9 = 1575
Now we have a system of two equations:
1. (S + W) * 7 = 1575
2. (S - W) * 9 = 1575
We can solve this system to find the values for S and W.
Let's simplify equation 1 by dividing both sides by 7:
S + W = 225
Now let's simplify equation 2 by dividing both sides by 9:
S - W = 175
We can solve this system of equations by adding them together:
(S + W) + (S - W) = 225 + 175
2S = 400
S = 200
So, the speed of the plane in still air is 200 miles per hour.
To find the speed of the wind, we can substitute the value of S into equation 1:
200 + W = 225
W = 225 - 200
W = 25
Therefore, the speed of the wind is 25 miles per hour.