An airplane can fly with the wind a distance of 920 miles in 4 hours. however, the return trip against the wind takes 5 hours. find the speed of the plane in still air and the speed of the wind.

speed of plane in still air=207 miles/hr

Speed of air=23 miles/hr

Explanation:

let the speed of plane in still air=u

speed of wind=v

speed of airplane with the wind= u+v

so time taken= t= d/(u+v)

d= distance=920 miles

t=4 hours

so 4= 920/(u+v)

u+v=230 (1)

speed of airplane against the wind= u-v

so time taken= t= d/(u-v)

d= distance=920 miles

t=5 hours

so 5= 920/(u-v)

u-v=184 (2)

Adding equations (1) and (2)

u+v +u-v=230+184

2u=414

u=207 miles/hr

now u+v=230

207+v=230

v=23 miles/hr

so speed of airplane in still air= 207 miles/hr

speed of wind= 23 miles/hr

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