A plane takes 3 hours to travel 1500 miles with the wind. it can travel only 1380 miles against the wind in the same amount of time. Find the speed of the wind and the speed of the plane in still air.
If the plane's speed is p, and the wind's speed is w, then since distance = speed * time,
3(p+w) = 1500
3(p-w) = 1380
Now you can easily find p, and then w.
To find the speed of the wind and the speed of the plane in still air, we can set up a system of equations based on the given information.
Let's denote the speed of the plane in still air as "p" and the speed of the wind as "w".
For the plane flying with the wind:
Distance = Speed × Time
1500 miles = (p + w) × 3 hours ----> Equation 1
For the plane flying against the wind:
Distance = Speed × Time
1380 miles = (p - w) × 3 hours ----> Equation 2
Now, we have a system of two equations with two variables. We can solve them simultaneously to find the values of "p" and "w".
Let's begin by rearranging Equation 1 and Equation 2:
Equation 1: 3p + 3w = 1500
Equation 2: 3p - 3w = 1380
Adding Equation 1 and Equation 2 cancels out the "w" term:
(3p + 3w) + (3p - 3w) = 1500 + 1380
6p = 2880
p = 2880 / 6
p = 480
Now that we have the value of "p," we can substitute it back into either Equation 1 or Equation 2 to find the value of "w". Let's substitute it into Equation 1:
3p + 3w = 1500
3(480) + 3w = 1500
1440 + 3w = 1500
3w = 1500 - 1440
3w = 60
w = 60 / 3
w = 20
Therefore, the speed of the plane in still air is 480 miles per hour, and the speed of the wind is 20 miles per hour.