A plane traveled 510
mph with the wind and 470
mph against the wind. Find the speed of the plane in still air and the speed of the wind
let speed of plane be x mph
let the speed of the wind be y mph
x+y = 510
x-y = 470
how about adding these two and see what happens.
To find the speed of the plane in still air and the speed of the wind, we can set up a system of equations.
Let's denote the speed of the plane in still air as "p" and the speed of the wind as "w".
When the plane is flying with the wind, the effective speed is the sum of the plane's speed in still air and the speed of the wind:
p + w = 510 mph --------- Equation 1
Similarly, when the plane is flying against the wind, the effective speed is the difference between the plane's speed in still air and the speed of the wind:
p - w = 470 mph --------- Equation 2
Now we have a system of two equations. We can use any method (substitution, elimination) to solve this system.
Let's solve it using the elimination method:
Adding the two equations together, we get:
(p + w) + (p - w) = 510 + 470
2p = 980
Dividing both sides by 2, we find:
p = 490 mph
Substituting this value back into Equation 1, we can solve for the speed of the wind:
490 + w = 510
w = 510 - 490
w = 20 mph
Therefore, the speed of the plane in still air is 490 mph, and the speed of the wind is 20 mph.