A plane traveled 400 miles to Rome and back.
The trip there was with the wind. It took 5 hours. The trip back was into the wind. The trip back took 10 hours.
- Find the speed of the plane in still air and the speed of the wind.
I think reiny already answered the same question. Look at related questions below
I can't find it
Can you post the link
http://www.jiskha.com/display.cgi?id=1470968772
thank you
Do you see Related Questions below these responses? I just clicked on the first in the list, and there it was!
To find the speed of the plane in still air and the speed of the wind, we can use the concept of relative speed.
Let's assume the speed of the plane in still air is represented by "p" and the speed of the wind is represented by "w".
When traveling 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 the effective speed is p + w.
Similarly, when traveling against the wind, the effective speed of the plane is the difference between its speed in still air and the speed of the wind. So the effective speed is p - w.
We know that the plane traveled 400 miles to Rome and back. So the total distance covered is 400 miles.
On the trip to Rome, the plane traveled with the wind at an effective speed of p + w, and it took 5 hours. Therefore, the distance traveled is equal to the speed multiplied by the time: (p + w) * 5 = 400.
On the trip back, the plane traveled against the wind at an effective speed of p - w, and it took 10 hours. So the distance traveled is: (p - w) * 10 = 400.
Now, we have a system of two equations:
1. (p + w) * 5 = 400
2. (p - w) * 10 = 400
We can solve this system of equations to find the values of p and w.
Expanding the equations, we get:
1. 5p + 5w = 400
2. 10p - 10w = 400
Simplifying equation 2, we divide both sides by 10:
2p - 2w = 40
Now we can solve this system of linear equations using any method like substitution or elimination.
Let's use elimination. Multiply equation 1 by 2:
10p + 10w = 800
Now, subtract equation 2 from the modified equation 1:
10p + 10w - (2p - 2w) = 800 - 40
Simplifying:
8p + 12w = 760
Divide both sides by 4 to simplify further:
2p + 3w = 190
Now we have simplified the system of equations to:
2p + 3w = 190 (equation 3)
2p - 2w = 40 (equation 4)
Subtract equation 4 from equation 3 to eliminate p:
(2p + 3w) - (2p - 2w) = 190 - 40
Simplifying:
5w = 150
Now we can solve for w by dividing both sides by 5:
w = 150 / 5
w = 30
So the speed of the wind is 30 mph.
Now substitute the value of w into either equation 3 or 4 to find p:
2p + 3(30) = 190
Expanding:
2p + 90 = 190
Subtract 90 from both sides:
2p = 190 - 90
2p = 100
Divide both sides by 2:
p = 100 / 2
p = 50
So the speed of the plane in still air is 50 mph.
Therefore, the speed of the plane in still air is 50 mph, and the speed of the wind is 30 mph.