SOLUTION: A plane takes 2 hr to travel 1060 mi with the wind. It can travel only 900 mi against the wind in the same amount of time. Find the speed of the wind and the speed of the plane in
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Question 1126709: A plane takes 2 hr to travel 1060 mi with the wind. It can travel only 900 mi against the wind in the same amount of time. Find the speed of the wind and the speed of the plane in still air. Found 2 solutions by ikleyn, Alan3354:Answer by ikleyn(52915) (Show Source):
The effective speed of the plane flying with the wind is = 530 miles per hour.
From the other side, it is the sum of the plane speed at no wind PLUS the speed of the wind.
It gives you your first equation
u + v = 530. (1)
The effective speed of the plane flying against the wind is = 450 miles per hour.
From the other side, it is the difference of the plane speed at no wind and the speed of the wind.
It gives you your second equation
u - v = 450. (2)
So you have the system of two equations in two unknowns (1) and (2).
To solve the system, add the two equations. You will get
2u = 530 + 450 = 980
u = 980/2 = 490.
Then from eq(2), v = 530 - 490 = 40.
Answer. The speed of the plane at no wind is 490 miles per hour.
The speed of wind is 40 miles per hour.
Solved.
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It is a typical "tailwind and headwind" word problem.
