Against a headwind, steve computes his flight tiem for a tripof 2900 miles at 5 hours. The flight would take 4 hours and 50 minutes if the headwind were half as much. Calculate the wind speed and the planes speed in the still air.

gemuntertjx

gemuntertjx

Answered question

2022-09-03

Against a headwind, steve computes his flight tiem for a tripof 2900 miles at 5 hours. The flight would take 4 hours and 50 minutes if the headwind were half as much. Calculate the wind speed and the planes speed in the still air.

Answer & Explanation

Kristopher Beard

Kristopher Beard

Beginner2022-09-04Added 18 answers

Against a headwind, steve computes his flight tiem for a tripof 2900 miles at 5 hours.
so, speed against head wind is:- 2900/5 = 580miles/hr
The flight would take 4 hours and 50 minutes = 29/6hr if the headwind were half as much.
so, speed against head wind half as much as before is:-2900/(29/6) miles/hr = 600 miles/hr
let, X miles/hr = speed of plane,
Y miles/hr = speed ofwind
so, speed against head wind = (X - Y) miles/hr
speed against head wind half as much as before is = (X - Y/2)miles/hr
so, we get,
X- Y = 580....................(1)
X - Y/2 = 600.................(2)
by (1) -(2) -Y + Y/2= -20
=> -Y/2 = -20
=> Y = 40
so, X = 580 - Y = 580 - (-40) = 620
so, speed of plane in stillwind = X = 620 miles/hr
speed ofwind = Y = 40 miles/hr

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