Find the rate of the wind.

Question

A plane can fly 180 mph in calm air. Flying with the wind, the plane can fly 594 mi in the same amount of time it takes to fly 486 mi against the wind. Find the rate of the wind.

Answer 1

 

 X is the speed of the wind.

 

 With the wind:

    594 = (180 +x)*t

 

Against the wind:

  486 = (180-x)*t

 

Solving each equation for t:

 

594/(180+x) = 486/(180-x)  <--- the times are the same

 

594(180-x) = 486(180+x)

 

106920  - 594X = 87480 + 486X

 

106920 - 87480 = 486X + 592X

 

19440 = 1080X

 

X = 18

 

The speed of the wind is 18 mph

 

The plane flies 594 miles in 3 hours with the wind.

The plane flies 486 miles in 3 hours against the wind. 

 

 

 

Answer 2

Hi Jayme:

 

Distance = Rate*Time

d = rt  ...   t = d/r

 

Let plane speed = p = 180

wind speed = w

 

With wind:  t = 594/(180+w)

Against wind:  t = 486/(180-w)

 

Since the time is the same:

 

594/(180+w) = 486/(180-w)

cross multiply

486(180+w) = 594(180-w)

87480 + 486w = 106920 - 594w

 

Finish solving for w to find wind speed