Airplane rate of change problem

Question

Flying against the wind, a plane travels 2,000 km in 5 hours. Flying with the wind, the plane travels the same distance in 4 hours. The speed of the wind is s kilometers per hour. What is the value of s?

Answer 1

The equation for this type of problems is distance = rate x time

Let x = speed of the plane in still air

Let s = speed of the wind

Since with the wind adds onto the speed, the rate with the wind is x+s

When going against the wind, it slows the plane down. So against the wind the rate is x-s

Using the information provided, there are 2 equations for this problem

2000=4(x+s) (With the wind)

2000=5(x-s) (Against the wind)

2 equations 2 unknowns can be solved using elimination or substitution. I chose elimination. First distribute.

2000=4x+4s

2000=5x-5s

Then multiply

5(2000=4x+4s)

4(2000=5x-5s)

10000=20x+20s

8000=20x-20s

Add the equations together, s term cancels out

18000=40x

Divide both sides by 40

x=450

But, the problem asks for s. So plug in x into either of the original equations.

2000=4(x+s)

2000=4(450+s) Divide both sides by 4

500=450+s Subtract both sides by 450

50=s