Question

A man flies a small airplane from fargo to bismarck, north dakota—a distance of 180 mi. because he is flying into a head wind, the trip takes him 2 h. on the way back, the wind is still blowing at the same speed, so the return trip takes only 1 h 15 min. what is his speed in still air, and how fast is the wind blowing?

Answer 1

when plane is moving in head wind condition we will have

`V_(plane) - v_(wind) = (distance)/(time)`

`V_(plane) - v_(wind) = (180)/(2)`

`V_(plane) - v_(wind) = 90 mph`

now when wind is tail wind condition during return journey we will have

time = 1 h 15 min = 1.25 hour

`V_(plane) + v_(wind) = (distance)/(time)`

`V_(plane) + v_(wind) = (180)/(1.25 )`

`V_(plane) + v_(wind) = 144 mph`

Now add both equations

`V_(plane) = 117 mph`

`v_(wind) = 27 mph`