Airplane speed and wind speed

Question

An airplane travels 5013 km against the wind in 9 hours and 5913 km with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

Hi Ryan,

 

For this distance rate time problem we have the following.

d = rt

 

t = 9 hours

d1 = 5013 km

d2 = 5913 km

r1 = speed of plane - wind speed = r-w

r2 = speed of plane + wind speed = r+w

 

So.

5013 = 9(r-w)

5913 = 9(r+w)

 

Distributing

5013 = 9r - 9w

5913 = 9r + 9w

 

Using the addition method we can eliminate the wind variable and solve for r

10926 = 18r

r = 607

 

Use this value of r in either of the original equations and solve for w

5013 = 9(607) - 9w

450 = 9w

w = 50

 

Plane speed in still air is 607 km/h

Wind speed is 50 km/h

 

Answer 2

Use Rate x Time = Distance (r=rate in still air, w= wind rate)

Therefore:

 

(r-w)9=5013

(r+w)9=5913

 

9r-9w=5013

9r+9w=5913   Distributive Property

 

Add the two equations. (It's a system!)

 

18r=10,928

 

r=607 for rate in still air.

w=50 if you substitute 607 for r in any equation above.

 

That's your answer!