Question

an airplane travels 1104 kilometers against the wind in 2 hours and 1344 kilometers 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

1) Gathering the data

Against the wind:

1104 km in 2 hours

With the wind:

1344 km in 2 hours

2) Let's set then, two equations to find the rate of the plane. Considering the speed of the plane and the wind are pulling the plane

With the wind:

2( plane + wind) = 1344 ⇒ 2(p+w) = 1344 ⇒ 2p+2w = 1344

Against the wind:

2( plane - wind) =1104 ⇒ 2(p-w) =1104 ⇒ 2p -2w=1104

So we can write this linear system of equations, and then add both equations simultaneously:

2p+2w = 1344

2p -2w=1104

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

4p =2408 Divide both sides by 4

p=602

Plugging into one equation the value of p, to find w:

2p -2w =1104

2(602) -2w = 1104

1204-2w=1104

-2w=1104-1204

-2w=-100

2w=100

w=50

3) As it is a rate, then we can write Speed of the plane = 602 km/h and Speed of the wind = 50km/h