Systems of linear equations

Question

When a plane flies with the wind, it can travel 2160 mikes in 3 hours. When it flies in the opposite direction it takes 4 hours to fly the same distance. Find the rate of the plane in still air and the rate of the wind.

Answer 1

Distance = Rate*Time

 

Our distance both ways is 2160 miles

Rate with the wind is plane speed plus wind speed = p+w

Rate against the wind is plane speed minus wind = p-w

 

3(p+w)=2160

4(p-w)= 2160

 

3p + 3w = 2160   equation 1

4p - 4w = 2160    equation 2

 

multiply equation 1 by 4

multiply equation 2 by 3

add the two equations together

 

12p + 12w = 8640    4(equation 1)

12p - 12w = 6480     3(equation 2)

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24p = 15,120

 

p = 15,120/24

p = 630 mph

 

3p+3w = 2160

3(630) + 3w = 2160

1890 + 3w = 2160

3w = 270

w = 90

 

plane speed is 630 mph

wind speed is 90 mph