Word problem

Question

Flying with the wind a plane went 183 km/hr. Flying into the same wind the plane went 141 km/hr. Find the speed of the wind and the speed of the plans in still air

Answer 1

Hi Ivy.

 

The key here is knowing that when a plane flies "with the wind", the wind is at is tail, PUSHING it so that it goes its own speed plus the speed of the wind.

 

Likewise, when a plane flies "into the wind", the wind is pushing the plane back, instead of helping it forward like above.  So when the plane flies INTO the wind, the plane's ground speed is not its actual speed, but the speed it would be flying  minus the speed at which the wind pushed is back.

 

So if we let  

 

S= plane's speed in still air

 

and 

 

W = the speed of the wind

 

we get two equations:

 

S + W = 183  

(wind pushing on the tail, making the plane travel faster)

and

S - W = 141

(wind pushing on the nose of the plane, slowing it down)

 

Solve this system of equations and you will have your answer.

 

 

Using elimination, add vertically and the "W"s go away, leaving

 

2S =324

 

Divide both sides by 2 and get

 

S = 162    So the plane's speed in still air is 162 km/hr

 

Substitute this back into either equation and get

 

S+W=183

162 + W = 183

 

Subtract 162 from both sides

 

W = 21   So the wind speed is 21 km/hr.