SOLUTION: A plane flies 720 miles against the wind in 3 hours. The return trip with the wind takes only 2 1/2 hours. Find the speed of the wind. Find the speed of the plane in still air. Ca
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Question 414498: A plane flies 720 miles against the wind in 3 hours. The return trip with the wind takes only 2 1/2 hours. Find the speed of the wind. Find the speed of the plane in still air. Can you show me how to set this problem and how to work it please? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A plane flies 720 miles against the wind in 3 hours.
The return trip with the wind takes only 2 1/2 hours.
Find the speed of the wind.
Find the speed of the plane in still air
:
Let s = speed of the plane in still air
Let w = speed of the wind
:
Then we can say
(s+w) = effective speed with the wind
and
(s-w) = effective speed against the wind
:
Write a distance equation for each trip; dist = time * speed
2.5(s+w) = 720
and
3(s-w) = 720
:
We can simplify this and use elimination to solve this
divide the 1st equation by 2.5
s + w =
s + w = 288
and
divide the 2nd equation by 3
s - w =
s - w = 240
:
Add these two equations.
s - w = 240
s + w = 288
----------------addition eliminates w, find s
2s = 528
s =
s = 264 mph is the plane speed in still air
:
Find w using the equation: s + w = 288
264 + w = 288
w = 288 - 264
w = 24 mph is the wind speed
:
Check solutions in the 2nd original equation: 3(s-w) = 720
3(264 - 24) =
3 * 240 = 720 mi confirms our solutions of s = 264, w = 24
