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A man flies a small airplane a distance of 180 mi. Because he is flying into head wind, the trip takes him 2 hours.
On the way back the wind is still blowing at the same speed so the return trip only takes 1 hr and 12 min.
What is his speed in the still air? How fast is the wind blowing
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When the man covered 180 mi in 2 hours flying into head wind, the speed of the plane relative to the ground was = 90 mph.
This speed is the difference of the plane speed in the still air "u" and the wind's speed "v":
= 90 = u - v. (1)
When the man covered the same distance of 180 mi in 1 hour 12 minutes in the return trip flying with the wind,
the speed of the plane relative to the ground was = 150 mph.
Here 1.2 = 1.2 hour = 1 hour and 12 minutes. (12 minutes = hour = 0.2 hour).
This speed is the sum of the plane speed in the still air "u" and the wind's speed "v":
= 150 = u + v. (2)
So you have this two equations to find u and v:
u - v = 90 (1')
u + v = 150. (2')
The simplest way to solve this system is to add the equations (1') and (2').
If you do, you will get
2u = 90 + 150, or 2u = 240. Hence, u = = 120.
Thus the speed of the plane in the still air is 120 mph.
Having this, you can easily find the speed of the wind v from the equation (1'):
v = u = 90 = 120 - 90 = 30 mph.
Answer. The speed of the plane is still air is 120 mph.
The speed of the wind is 30 ph.
Solved.
What I wrote here is the standard way of solving this type of problems and the standard way of explaining the solution.
For more solved problems of this type see the lessons
- Wind and Current problems
- More problems on upstream and downstream round trips
- Wind and Current problems solvable by quadratic equations
- Unpowered raft floating downstream along a river
- Selected problems from the archive on the boat floating Upstream and Downstream
- Selected problems from the archive on a plane flying with and against the wind
in this site.
Please be informed that you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.