a jet flies with wind at 1100 km/h and against the same wind at 750 km/h.Find the rate of the wind and the speed of the jet in still air.
Let y = wind speed and x = plane speed
x + y = 1100
x - y = 750
Add the two equations.
2x = 1850
x = ?
Solve for x. Insert value into one equation to find y. To check, insert both values into other equation.
x=925
To find the rate of the wind and the speed of the jet in still air, we can set up a system of equations based on the given information.
Let's denote the speed of the jet in still air as "j" and the rate of the wind as "w".
When the jet flies with the wind, the effective speed is the sum of the speed of the jet and the speed of the wind: j + w.
Therefore, we can set up the equation:
j + w = 1100 km/h -- (1)
Similarly, when the jet flies against the wind, the effective speed is the difference between the speed of the jet and the speed of the wind: j - w.
Therefore, we can set up the equation:
j - w = 750 km/h -- (2)
Now we have a system of two equations with two variables (j and w). We can solve this system to find the values of j and w.
To do that, we can use the method of elimination. We eliminate the variable "w" by adding the two equations together:
(j + w) + (j - w) = 1100 km/h + 750 km/h
2j = 1850 km/h
Dividing both sides by 2, we get:
j = 925 km/h
Now, we can substitute the value of j back into one of the original equations (Equation 1 or 2) to solve for w.
Using Equation 1, we have:
925 km/h + w = 1100 km/h
Subtracting 925 km/h from both sides, we get:
w = 175 km/h
Therefore, the rate of the wind is 175 km/h and the speed of the jet in still air is 925 km/h.
In summary:
- Rate of the wind: 175 km/h
- Speed of the jet in still air: 925 km/h