Asked by Ed
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?
Answers
Answered by
Reiny
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
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
Answered by
Anonymous
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