A pilot flew a 400-mile flight in 2.5 hours flying into the wind. Flying the same rate and with the same wind speed, the return trip took only 2 hours, with a tailwind.
What was the speed of the wind?
the correct answer is 20 miles per hour. I just answered 40 and it counted it wrong and said it was 20. Good luck
The correct answer is 20.
To find the speed of the wind, we need to use the concept of relative speed.
Let's assume the speed of the plane in still air (with no wind) is P, and the speed of the wind is W.
When the pilot was flying into the wind, the effective speed of the plane relative to the ground would be reduced. Therefore, the speed of the plane flying into the wind would be P - W.
Given that the distance of the flight is 400 miles and the time taken is 2.5 hours, we can set up the equation:
Distance = Speed × Time
400 = (P - W) × 2.5
Similarly, when the pilot was flying with a tailwind (the wind pushing the plane from behind), the effective speed of the plane relative to the ground would be increased. Therefore, the speed of the plane flying with the tailwind would be P + W.
Given that the return trip took 2 hours, we can set up another equation:
400 = (P + W) × 2
Now, we have a system of two equations:
1) 400 = (P - W) × 2.5
2) 400 = (P + W) × 2
We can solve this system of equations to find the values of P (speed of the plane) and W (speed of the wind).
Let's start by solving equation 1 for P - W:
400/2.5 = P - W
160 = P - W
Next, solve equation 2 for P + W:
400/2 = P + W
200 = P + W
Now, we have a system of two equations:
160 = P - W
200 = P + W
Add these two equations together:
160 + 200 = P - W + P + W
360 = 2P
Divide both sides by 2:
360/2 = 2P/2
180 = P
Now that we know the value of P (the speed of the plane), we can substitute it back into one of the equations to find the value of W (the speed of the wind).
Using equation 2:
400 = (180 + W) × 2
Divide both sides by 2:
400/2 = (180 + W) × 2/2
200 = 180 + W
Subtract 180 from both sides:
200 - 180 = W
20 = W
Therefore, the speed of the wind is 20 miles per hour.
since distance=speed*time,
(p-w)(2.5) = 400
(p+w)(2) = 400
Now just solve for w, the wind speed.