a plane travels 1800 miles with a head speed in 16 hours. the plane takes 9 hours to travel the same distance in 9 hours. what is the speed of the plane and air

Question

R= speed of plane in still air

C= speed of wind

Answer 1

I assume the 9 hours was the return trip with a tail wind.

 

d = rt   distance = rate(time)

 

Using c = wind speed, r = plane speed:

 

With head wind: 

distance = 1800

rate = plane speed minus wind speed = r-c

time = 16

1800 = 16(r-c)   

16r - 16c = 1800 {equation 1}

 

With tail wind:

distance = 1800

rate = plane speed plus wind speed = r+c

time = 9

1800 = 9(r+c)

9r + 9c = 1800

r + c = 200       {equation 2}

 

16r - 16c = 1800

r + c = 200

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multiply 2nd equation by 16 and add equations

 

16r - 16c = 1800

16r + 16c = 3200

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32r = 5000

r = 156.25 mph

 

 

r + c = 200

156.25 + c = 200

c = 200 - 156.25

c = 43.75 mph

 

Check:

1800 = 16(r-c)

1800 = 16(156.25-43.75)

1800 = 1800  

 

1800 = 9(r+c)

1800 = 9(156.25+43.75)

1800 = 1800

 

Answer fits the criteria given