posted by Ed on .
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?
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
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