SOLUTION: The airspeed of a plane is its speed through the air. The groundspeed of a plane is its speed relative to the ground. The groundspeed of an airplane is affected by the speed of the
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Question 1073014: The airspeed of a plane is its speed through the air. The groundspeed of a plane is its speed relative to the ground. The groundspeed of an airplane is affected by the speed of the wind. Suppose that a plane flying 1800 miles west requires 9 hours and flying 1800 miles east requires 6 hours. Find the airspeed of the plane and the effect wind resistance has on the plane. Answer by ikleyn(52847) (Show Source):
Let u be the airspeed and v be the speed of the wind.
Then the ground-speed flying east (with the wind) is (u+v),
while ground-speed flying west (against the wind) is (u-v).
The condition gives you these two equations:
= u - v (1) (flying west against the wind) and
= u + v (2) (flying east against the wind).
It is the same as
u - v = 200, (3)
u + v = 300. (4)
Add equations (3) and (4) (both sides). You will get
2u = 200 + 300 = 500. Hence, u = = 250 miles per hour is the airspeed.
Then from (4) u = 300 - 250 = 50 miles per hour is the speed of the wind.
Solved.
It is a typical "tailwind and headwind" word problem.
In these lessons you will find the detailed solutions of many similar problems.
Consider them as samples. Read them attentively.
In this way you will learn how to solve similar problems once and for all.
