Air speed problem

[tmraz]

Good afternoon,
I am helping a library patron with an algebra problem and I needed some assistance. The problem is as follows:
If an airplane takes 2 hours to travel 600 km against a head wind and the return trip take 1 2/3 hours with the wind. Find the speed.
How would you set up this problem? Thank you in adavance for your help.

 

[Aladdin]

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V=d/t

V= 600/2 = 300 km/h.

V= (600)/(5/3) = 360 km/p

V(average) = 330 km/h .

 

[mmm4444bot]

Find the speed. Find the speed of what?

The airplane in still air?

The wind?

Both?

I suspect that the instructor wants to see a system of equations solved, for this exercise. But, that's a guess, on my part.

Here's the set-up, for finding the airplane's speed in still air and the wind speed.

Let A = the speed of the plane in still air

Let W = the speed of the wind

When the plane flies against the wind, its speed in still air is reduced by the speed of the wind pushing against it.

Plane's net rate flying against the wind: A - W.

When the plane flies with the wind, its speed in still air is increased by the speed of the wind pushing it along.

Plane's net rate flying with the wind: A + W

DISTANCE = RATE * TIME

600 = (A - W)(2)

600 = (A + W)(5/3)

This is a system of two equations in A and W.

The solution gives the value of A (speed of plane in still air) and W (wind speed).