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- anonymous

I have a distance problem and I know the equation is d=rt. I'm just not sure how to solve the problem: A flight crew flew 420 km in 3 h with a tailwind. Flying against the wind, the flight crew flew 440 km in 4 h. Find the rate of the flight crew in calm air and the rate of the wind.

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- anonymous

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- anonymous

the total distance traveled divide by total amount time should give you an average of how much traveled per hour

- anonymous

so it would be 420/3? and 440/4 to get the rate?

- anonymous

since you are looking for a rate of travel in calm air, i think (420+440)/(3+4) should do it

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- anonymous

ok Thank you so much!!

- anonymous

How would I find the rate of the wind?

- anonymous

is the rate of the wind considered same for both cases?

- anonymous

I guess it would be....the answer I get for the first part is 122.8 km/h. Do I use that answer to determine the rate of the wind?

- anonymous

one way to find out is - since you have the rate of travel at calm wind, you can subtract rate of travel at either tail wind or against the wind from calm wind

- anonymous

wind=15 km/hr, aircraft speed = 125 km/hr

- anonymous

i don't think you can just add the rate of travel since the time at which air plane travels is different

- anonymous

i think the rate of wind might be different for both cases

- anonymous

@robtobey, how did you arrive at 125 km/h = aircraft speed and 15 km/hr = wind? Was the original equation wrong or was mymath wrong? :)

- anonymous

msayer3,
There is no indication from the problem statement that the wind velocity changed from my point of view.

- anonymous

yeah, that's what i'm wondering.

- anonymous

I will post the solution in a few minutes.

- anonymous

ok...thank yo very much

- anonymous

r*t = d
r = d/t
Let x = the wind speed
First flight leg:
\[r+x==\frac{d}{t}\text{/.} \{d\to 420,t\to 3\} \]r + x = 140
Second flight leg:\[r-x=\frac{d}{t}\text{/.} \{d\to 440,t\to 4\} \]r - x = 110
2 r = 140 + 110
r = 125
r + x =140
125 + x = 140
x = 15

- anonymous

I use Mathematica for the calculations
/. means sort or, "replace the symbols as follows"

- anonymous

Ok...I think I got it now. Thank you again for your help.

- anonymous

Glad I could help you out.

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