the jetstream is a strong wind current that flows across the united states. flying with the jetstream, a plane flew 3,000 miles in 5 hours. Against the same wind, the trip took 6 hours. Find the airspeed of the plane (the speed in still water).
My answer:
X=550 miles per hour
correct
(the jet stream does not just flow over the US )
To find the airspeed of the plane, we need to separate the effect of the wind from the actual speed of the plane. Let's assume the speed of the plane in still air (airspeed) is "X" miles per hour.
First, let's analyze the flight with the jetstream. The plane flew 3,000 miles in 5 hours. Since it was flying with the wind, the wind speed provided an additional boost to the plane's speed. So, the effective speed of the plane with the jetstream is X + W, where W represents the speed of the jetstream.
Using the formula: Speed = Distance / Time, we can write the equation for the flight with the jetstream as: (X + W) = 3,000 miles / 5 hours.
Now, let's consider the flight against the wind. The plane still traveled 3,000 miles, but this time it was flying against the wind. The wind speed now acts as a hindrance, so the effective speed of the plane against the wind is X - W.
Using the same formula, we can write the equation for the flight against the wind as: (X - W) = 3,000 miles / 6 hours.
Now, we have a system of two equations with two unknowns (X and W):
1) (X + W) = 3,000 / 5
2) (X - W) = 3,000 / 6
To solve this system of equations, we can use simple algebraic manipulation.
First, let's find the value of X by adding the two equations together:
(X + W) + (X - W) = 3,000 / 5 + 3,000 / 6
2X = 600 + 500
2X = 1,100
Dividing both sides of the equation by 2, we get:
X = 550
So, the airspeed of the plane (the speed in still water) is 550 miles per hour.