SOLUTION: When a plane flies with the wind, it can travel 420 miles in 1.5 hours. When the plane flies in the opposite direction, against the wind, it takes 2 hours to fly the same distance.

Question 1137148: When a plane flies with the wind, it can travel 420 miles in 1.5 hours. When the plane flies in the opposite direction, against the wind, it takes 2 hours to fly the same distance. Find the average velocity of the plane in still air and the average velocity of the wind.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
When a plane flies with the wind, it can travel 420 miles in 1.5 hours.
When the plane flies in the opposite direction, against the wind, it takes 2 hours to fly the same distance.
Find the average velocity of the plane in still air and the average velocity of the wind.
:
let s = the plane speed in still air
let w = velocity of the wind
then
(s+w) = ground speed with the wind
and
(s-w) = ground speed against
:
Write a distance equation for each scenario; dist = time * speed
1.5(s+w) = 420
2.0(s-w) = 420
we can simplify both equations, divide the 1st by 1.5, divide the 2nd by 2
s + w = 280
s - w = 210
---------------addition eliminates w, find s
2s + 0 = 490
s = 490/2
s = 245 mph in still air
and
245 + w = 280
w = 280 - 245
w = 35 mph is velocity of the wind
;
:
Confirm these solution in the 1st original equation
1.5(245 + 35) =
1.5(280) = 420
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