Question

Against the Wind a small plane flew 858 miles in 2 hours and 10 minutes the return trip only took 1 hour and 50 minutes what was the speed of the wind?what was the speed of the plane in still air?​

Answer 1

• The speed of the plane - 432 miles/ hr.
• The speed of the wind - 36 miles/ hr.

Define the relation of speed and time?

• A moving body's speed is the distance it travels in one unit of time. If the distance is in kilometers and the duration is in hours, the speed is in kilometers per hour.
• If a distance is measured in meters and the time is measured in seconds, the speed is measured in meters per second.

Let the speed of the small plane be 'R'.

Let the speed of the wind be 'S'.

Plane's time against wind = 2 hours and 10 minutes  = 13/6 hours.

Plane's time with wind = 1 hour and 50 minutes = 11/6 hours

Use formula;

Distance =  speed x time

Against the wind:

858 = (13/6) (R-S)  = (13/6) R - (13/6)S

With wind:

858 = (11/6)(R + S) = (11/6)R + (11/6)S  

Multiplies each by 6.

5148 = 13R - 13S

5148 = 11R + 11S

Use elimination method

56628 = 143R - 143S  (multiplies by 11)

66924 = 143R + 143S  (multiplies by 13)

Further solving;

123552 = 276R

R = 432 miles/ hr. (speed of small plane )

And,  S = 36 miles/ hr. (speed of wind)

To know more about the speed and time, here

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