A plane will normally cover 52 km in 12 min in still air. On one trip she flew with the wind for 2.5 hr. returning, she still had 100 km to go after 3.5 hr. what was the wind speed?
To find the wind speed, you can use the concept of relative velocity. The speed of the plane with respect to the wind is the difference between the speed of the plane in still air and the speed of the wind.
Let's break down the problem step by step:
1. Find the speed of the plane in still air: Since the plane covers 52 km in 12 minutes in still air, we need to convert this time to hours. There are 60 minutes in an hour, so 12 minutes is equivalent to 12/60 = 0.2 hours. Therefore, the speed of the plane in still air is 52 km / 0.2 hr = 260 km/hr.
2. Find the distance the plane traveled with the wind: The plane flew with the wind for 2.5 hours, so the distance it traveled is 260 km/hr * 2.5 hr = 650 km.
3. Find the remaining distance after the return trip: After 3.5 hours, the plane still had 100 km to go. Therefore, the total distance traveled in 3.5 hours is 650 km + 100 km = 750 km.
4. Find the time taken for the return trip: Since the total distance traveled is 750 km and the time taken is 3.5 hours, the average speed of the return trip is 750 km / 3.5 hr ≈ 214.29 km/hr.
5. Find the wind speed: Let's assume the wind speed is 'w' km/hr. The speed of the plane relative to the ground while flying against the wind is (260 km/hr - w km/hr). We can use this relative speed to find the time taken for the return trip. Since the remaining distance is 100 km and the speed is (260 km/hr - w km/hr), we have 100 km = (260 km/hr - w km/hr) * 3.5 hr.
Simplifying the equation: 100 km = (910 km - 3.5w km) ➞ rearranging the equation gives us 3.5w km = 910 km - 100 km ➞ 3.5w km = 810 km ➞ w km ≈ 231.4 km/hr.
Therefore, the wind speed is approximately 231.4 km/hr.