A jet travels at a rate of 798 mi/hr. with the wind. Going against the wind, the jet travels at a rate of 762 mi/hr. What is the rate of the jet in still air and the the rate of the wind?
please show how the equation should be set up
Vp + Vw = 798
Vp - Vw = 762
Solve using the elimination method.
Vp = Velocity of plane in still air.
Vw = Velocity of the wind.
To solve this problem, we can use the concept of relative speed. Let's assume the rate of the jet in still air is denoted by 'x' (in mi/hr), and the rate of the wind is denoted by 'y' (in mi/hr).
When the jet is traveling with the wind, its effective speed is increased by the speed of the wind. So, the equation for this scenario would be:
x + y = 798 (equation 1)
When the jet is traveling against the wind, its effective speed is decreased by the speed of the wind. So, the equation for this scenario would be:
x - y = 762 (equation 2)
Now, we have a system of two equations with two variables. To solve this system, we can use the method of substitution or elimination.
Let's solve it using the substitution method:
From equation 1, solve for x:
x = 798 - y
Substitute this value of x in equation 2:
798 - y - y = 762
Simplify the equation:
798 - 2y = 762
Rearrange the equation:
2y = 798 - 762
Simplify:
2y = 36
Divide both sides by 2:
y = 18
Now, substitute the value of y back into equation 1 to find x:
x + 18 = 798
Subtract 18 from both sides:
x = 798 - 18
Calculate:
x = 780
Therefore, the rate of the jet in still air is 780 mi/hr, and the rate of the wind is 18 mi/hr.