Distance word problem

Question

an airplane flying into a headwind travels the 1800 mile in 3.6 hours on the return trip the same distance is travled in 3 hours. Find the speed of the plane and the speed of the wing

Answer 1

To solve this we use the distance formula:

distance = rate*time  ...   d = rt

 

Let p = speed of plane in still air

Let w = speed of wind

 

1)  Flying into the headwind:

     the rate of travel = p-w

     1800 = 3.6(p-w)

 

2) Returning, flying with the wind:

    rate of travel = p+w

    1800 = 3(p+w)

 

3.6p - 3.6w = 1800     equation 1

3p+3w = 1800            equation 2

 

Multiply equation 1 by 2, multiply equation 2 by 2.4.

Add the new equations.

 

7.2p - 7.2w = 3600     ...  2(equation 1)

7.2p + 7.2w = 4320    ... 2.4(equation 2)

-------------------------

14.4p = 7920

 

p = 7920/14.4 = 550 mph

 

plug that back into original equation 2 and solve for w

 

3p + 3w = 1800

3(550) + 3w = 1800

1650 + 3w = 1800

subtract 1650 from both sides

3w = 150

divide both sides by 3

w = 150/3 = 50 mph

 

The plane speed is 550 mph

The wind speed is 50 mph