Airplane rate of change problem

Question

Flying against the wind, a plane travels 2,400 km in 6 hours. Flying with the wind, the plane travels the same distance in 4 hours. In the absence of wind, the speed of the plane is k kilometers per hour. What is the value of k?

Answer 1

Let w is speed of wind. Then k + w = 2400/4 = 600 and k - w = 2400/6 = 400.

So, we have system of equations: k + w = 600, k - w = 400. If we add we get 2k = 1000,

k = 500 km/h and now w = 600 - 500 = 100 km/h

Answer 2

We are working with the equation, d = rt (distance = rate x time)

Flying against the wind slows the plane down.

Flying with the wind allows the plane to fly faster.

Let's add one more variable, k, the speed of the wind.

The actual speed of the plane without wind is r.

The actual speed of the plane when travelling against the wind is r-k.

The actual speed of the plane when travelling with the wind is r+k.

We have two equations

2400 = (r-k)6

2400 = 4r

Use this 2nd equation to find r

r = 2400/4 = 600

Substitute this into the first equation.

2400 = (600-k)6

divide both sides by 6

400 = 600-k

We find that k = 200 km/hr.