Find the speed of the plane in still air and the speed of the wind.

Question

I would need help in solving this question because this is confusing for me to solve

 

A plane traveled 1110 miles with the wind in 2 hours and 918 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.

Answer 1

velocity = displacement/time

 

traveling with the wind means that the wind and the plane are in the same direction. Therefore it makes sense that the plane travels the same distance in shorter period of time. Let the velocity of the plane be V1 and the velocity of the wind be V2. Using the formula above,

 

V1+V2 = displacement/time = 1110/2 = 555 miles/hour

 

Now, when the plane moves against the wind, they are no longer in the same direction. Since velocity is a vector quantity, we have to represent one of them as negative. I will use negative sign for the wind.

 

So V1 - V2 = 918/2 = 459 miles/hour

 

 

Let's add up the two equations: V1+V2+V1-V2 = 555+459

 

So 2V1= 1014 ---> V1 = 1014/2 = 507 miles/hour

 

So V2 - 507-459 = 48 miles/hour

 

And we are done! Remember that speed is the absolute value of velocity. But I used velocity since the direction matters and when they are in opposite direction, one has to be negative. But our final answer is positive for both plane and wind velocity so that is the same as speed.