rate of wind and rate of plane in still air

Question

An airplane travels
3350km
against the wind in
5
hours and
3850km
with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

Hi Joyce and Timothy, this can be solved by a system of equations based on the information given. Let p represent the plane and w the wind.

 

Equation 1, with the wind:

 

5 * (p + w) = 3850

 

Equation 2, against the wind:

 

5 * (p - w) = 3350

 

Solve the system:

 

5 * (p + w) = 3850

5 * (p - w) =  3350

----------------------

 

Questions?

Answer 2

Figure out the speed in both cases by using r=d/t

So r₁ = 3350/5 and r₂ = 3850/5

The wind either slows the plane down or increases its speed by the same amount. So, to figure out the speed of the plane in still air, the speed will be the average of the two rates. Then you can also figure out how fast the wind is moving.