An airplane flying with the help of a strong tail wind covers 1200 km in 2 hours. In the return trip, while flying against the wind, it takes 2.5 hours to cover the same distance. How fast is the plane in still air and what is the speed of the wind?

Question

anonymous · Answer

How to solve it using 2 variables? (x and y)

anonymous · Answer

This can be solved with simultaneous equations. Let the the plane's speed in still air be x and the wind speed be y.

When flying with the wind, the plane's total speed is x+y, and when against the wind, its speed is x-y.

Then you can use the fact that speed = distance/time, to set up two equations in x and y - let me know if you need more help, but you should be able to solve it from there, I hope!

anonymous · Answer

@mojo872  I really don't get how to solve this. Can you explain how to solve this?

anonymous · Answer

when the airplane moves with the wind, its motion is supported by the wind movement. So its speed increases. now this increase can only be as much the wind velocity, since it is the wind providing this increase. Do you follow?

radar · Answer

Use the procedure suggested by mojo872.

Determine the speed with the wind using the fact that distance is equal to speed times time.  The speed with the wind is x+y, the speed also can be calculated by dividing the distance of 1200 km by 2 hours giving you 1200/2 = 600.  So equation 1. would be:
x + y = 600

You can do the same thing for the return trip which was against the wind. x - y.  Do it the same way, the distance is still 1200 km.

anonymous · Answer

speed of the plane with the wind = speed of plane in still air + wind speed
Speed 1 = x+y
Since, speed = distance / time
x + y = 1200 Km/ 2 hr
and similarly, speed of the plane against the wind = speed of plane in still air - wind speed
speed 2 = x-y
x-y = 1200 Km/ 2.5 hr

anonymous · Answer

$$x+y = 600$$$$x-y= 480$$solve  this system of equations for the values of x (speed of plane in still air) and y (wind speed).

anonymous · Answer

add both the equations and you'd see that y is eliminated leaving an equation in x (speed of the plane in still air) solve for the value of x and then substitute it in any of the equations to get the value of y (wind speed).

anonymous · Answer

thanks!