Posted by **Ed** on Thursday, February 16, 2012 at 7:51am.

2 airplanes start at the same time from airports 500 km apart. Each flies with an airspeed of 200 km/hr toward the other airport. One reaches its airport half an hour before the other plane reaches the other airport. How fast is the wind blowing?

- math -
**Reiny**, Thursday, February 16, 2012 at 9:01am
let the windspeed be x km/h

time going with the wind = 500/(200+x)

time going against the wind = 500(200-x)

the difference in those times = 1/2 hr

500/(200-x) - 500/(200+x) = 1/2

times 2(200-x)(200+x)

1000(200+x) - 1000(200-x) = (200-x)(200+x)

200000 + 1000x - 2000000 +1000x = 40000 - x^2

x^2 + 2000x - 40000 = 0

using the quadratic formula, I got

x = 19.8 or an unreasonable 2nd answer

the windspeed is 19.8 km/h

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