When an airplane flies with a given wind, it can travel 3000 km in 5hrs. When the same airplane flies in the opposite direction against the wind it takes 10hrs to fly the same distance. Find the speed of the plane in still air and the speed of the wind.
speed of plane in still air --- x km/h
speed of wind ---- y km/h
speed of plane with the wind --- x+y km/h
speed of plane against the wind -- x-y km/h
first fact:
5(x+y ) = 3000
x+y = 600 #1 equation
second fact:
10(x-y) = 3000
x-y = 300 #2 equation
add #1 + #2, it becomes so easy.
speed of a plane in still air is 450
speed of wind is 150
To find the speed of the plane in still air and the speed of the wind, we can use a system of equations. Let's assume the speed of the plane in still air is represented by "p" and the speed of the wind is represented by "w".
When the airplane flies with the wind, its effective speed is increased by the speed of the wind. So, the equation for this situation is:
(p + w) * 5 = 3000
When the airplane flies against the wind, its effective speed is decreased by the speed of the wind. So, the equation for this situation is:
(p - w) * 10 = 3000
Now we have a system of two equations with two variables. To solve it, we can use substitution or elimination method. Let's use the elimination method.
First, let's multiply the first equation by 2 to eliminate the "p" term:
2 * ((p + w) * 5) = 2 * 3000
10p + 10w = 6000
Now, let's subtract the second equation from the first equation to eliminate the "p" term:
(10p + 10w) - ((p - w) * 10) = 6000
10p + 10w - 10p + 10w = 6000
20w = 6000
w = 300
Now that we have the value for the wind speed, we can substitute it back into either of the original equations to find the value of "p".
Using the first equation:
(p + 300) * 5 = 3000
p + 300 = 600
p = 300
Therefore, the speed of the plane in still air is 300 km/hr, and the speed of the wind is 300 km/hr.