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.

Question

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.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

ok Thank you so much!!

anonymous · Answer

How would I find the rate of the wind?

anonymous · Answer

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

anonymous · Answer

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 · Answer

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 · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

@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 · Answer

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

anonymous · Answer

yeah, that's what i'm wondering.

anonymous · Answer

I will post the solution in a few minutes.

anonymous · Answer

ok...thank yo very much

anonymous · Answer

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 · Answer

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

anonymous · Answer

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

anonymous · Answer

Glad I could help you out.