Find the speed of the wind

Question

A plane has a cruising speed of 250 miles per hour when there is no wind. At this speed, the plane flew 300 miles With the wind in the same anount of time it flew 200 miles against the wind. Find the speed of the wind.

Answer 1

 

Let x = speed wind

Let t = time

 

Rate * time = distance ... the time is the same (according to problem specifications) ... the distance is provided 

 

     With the wind ... rate = 250 + x

     Against the wind ... rate = 250 - x 

 

We construct our equations ...

 

     WITH THE WIND:  

          rate * time = distance

          (250 + x) * t = 300

 

      AGAINST THE WIND:

           rate * time = distance

           (250 - x) * t = 200

 

We now have 2 equations ... we can solve both of then for the time.  That gives us these 2 equations

 

           t = 300/(250 + x)

 

           t = 200/(250 - x)

 

Using substitution, we end up with this 1 variable equation involving x:

 

           300/(250 + x) = 200(250 -x)

 

Solving for x ... x = 50 ... the speed of the wind