A JET FLIES WITH THE WIND AT 1100km/hr and 750 km/hr against the same wind.
Find the rate of the wind and speed of the plane
PLEASE INCLUDE THE EQUATION OR SET FOR SOLUTION
Eq1: Vp + Vw = 1100.
Eq2: Vp - Vw = 750.
Add the Eqs:
2Vp = 1850
Vp = 925 km/h = Velocity of the plane.
In Eq1, substitute 925 for Vp:
925 + Vw = 1100
Vw = 1100 - 925 = 175 km/h = Velocity of the wind.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the speed of the plane (in still air) is denoted by "p" and the speed of the wind is denoted by "w".
When the jet flies with the wind, the combined speed (plane's speed + wind's speed) is 1100 km/hr. Therefore, the equation for this scenario is:
p + w = 1100 (Equation 1)
Similarly, when the jet flies against the wind, the combined speed is 750 km/hr. So, the equation for this scenario is:
p - w = 750 (Equation 2)
Now, we have a system of two equations with two unknowns (p and w). We can solve this system to find the values of p (speed of the plane) and w (speed of the wind).
Method 1: Substitution Method
In Equation 1, isolate one of the variables (p or w) and substitute it into the other equation. Let's isolate p from Equation 1:
p = 1100 - w
Substitute this value of p into Equation 2:
(1100 - w) - w = 750
Simplifying:
1100 - 2w = 750
Subtract 1100 from both sides:
-2w = -350
Divide by -2:
w = 175
Substitute the value of w into Equation 1 to find p:
p + 175 = 1100
p = 925
Therefore, the speed of the wind is 175 km/hr, and the speed of the plane is 925 km/hr.
Method 2: Elimination Method
In this method, we'll eliminate one variable by adding or subtracting the two equations.
Add Equation 1 and Equation 2:
(p + w) + (p - w) = 1100 + 750
Simplifying:
2p = 1850
Divide by 2:
p = 925
Substitute the value of p into Equation 1 to find w:
925 + w = 1100
w = 175
Again, we find that the speed of the wind is 175 km/hr, and the speed of the plane is 925 km/hr.
Both methods lead to the same result, confirming that the speed of the wind is 175 km/hr, and the speed of the plane is 925 km/hr.