## anonymous 5 years ago 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.

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

ok Thank you so much!!

5. anonymous

How would I find the rate of the wind?

6. anonymous

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

7. 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?

8. 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

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. 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? :)

13. anonymous

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

14. anonymous

yeah, that's what i'm wondering.

15. anonymous

I will post the solution in a few minutes.

16. anonymous

ok...thank yo very much

17. 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

18. anonymous

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

19. anonymous

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

20. anonymous