What was the speed of the wind?

Question

flying from concrete, WA to Weed, CA is a 500 mile trip. If the airspeed of his plane is 200mph( travls 200mph in still air) and the total roundtrip (500 miles into the wind and 500 miles with the wind) takes 5 hour and 20 minutes, what was the speed of the wind?

Answer 1

Let w > 0 be the speed of the wind.

Traveling with the wind the plane is traveling at a speed of (200 + w)

Traveling against the wind the plane is traveling at a speed of (200 - w)

 

Total time is 5 1/3 = 16/3 hr, Let t be the time traveling with the wind.

Then the time traveling against the wind is (16/3 - t) = (16 - 3t)/3

 

Now 500 = t * (200 + w) = (16 - 3t)*(200 - w)/3

 

t = 500/(200 + w)

 

Then 1500 = (16 - 3t) * (200 - w)

        1500 = (16 - 1500/(200 + w)) * (200 - w)

        1500(200 + w) = (3200 + 16w - 1500) * (200 -  w)

        1500(200 + w) = (1700 + 16w) * (200 - w)

        4(75000 + 375w) = 4(425 + 4w) * (200 - w)

        75000 + 375w = 85000 + 375w - 4w²

        4w² = 10000

        w² = 2500

        w = 50 mph

 

The speed of the wind is 50 mph.

 

It took 2 hours traveling with the wind and 3 hours 20 minutes traveling against the wind.

 

 

 

Answer 2

Let speed of wind be "w" mph

plane speed with the wind = 200+ w  mph

plane speed into the wind = 200 - w   mph

 

Time to travel 500 miles with wind = 500/(200+w) hours

Time to travel 500 miles into the wind = 500/(200-w) hours

 

so

 

500/(200 + w)  +  500/(200-w)    = 5.3                           5 hours 20 minutes = 5.3 hrs

 

Solve for w

 

(500(200-w)   +  500(200+w))/(200+w)(200-w) = 5.3

 

100000 - 500w + 100000 + 500w = 5.3(200+w)(200-w)

 

200000 = 5.3(40000 - w²)

200000/5.3 = 40000 - w²

37735.85  = 40000 - w²

w² = 2264.15

w=47.58 mph