Question

It takes 6 hours for a plane to travel 720 km with a tail wind and 8 hours to make the return trip with a head wind. Find the airspeed of the plane and speed of the wind current

Answer 1

What are tail/head winds?

Answer 2

We know this is a distance, rate, time problem so d = rt is the appropriate formula to use. However since we have to consider both airspeed and wind speed, we'll have to alter the formula a bit.

a = airspeed
w = windspeed

\(r = a \pm w\)

Answer 3

So we'll use the formula \(d = (a \pm w)t\)

In other words, we need to use two separate formulas one for headwind, and the other for tailwind:
\(d = (a - w)t\)
\(d = (a + w)t\)

Answer 4

d = 720

For headwind, t = 8
For tailwind, t = 6

so:

\(720 = (a - w)8\)
\(720 = (a + w)6\)

Answer 5

Now divide the first equation by 8
Divide the second equation by 6

\(90 = a - w\)
\(120 = a + w\)

Answer 6

Now you have a systems of equations. You can finish solving using elimination method. Try solving for a

Answer 7

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Answer 8

What values did you get for a and w?

Answer 9

a=105 and w=15?

Answer 10

Good job