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Sagot :
Using the relation between velocity, distance and time, it is found that:
- The rate of the plane in still air is of 140 mph.
- The rate of the wind is of 40 mph.
What is the relation between velocity, distance and time?
Velocity is distance divided by time, that is:
[tex]v = \frac{d}{t}[/tex]
A plane traveling with the wind travels 900 miles in 5 hours, hence:
[tex]v_a + v_w = \frac{900}{5}[/tex]
[tex]v_a + v_w = 180[/tex]
The return trip is against the wind and takes 9 hours, hence:
[tex]v_a - v_w = \frac{900}{9}[/tex]
[tex]v_a - v_w = 100[/tex]
From the first equation, we have that:
[tex]v_w = 180 - v_a{/tex]
Replacing on the second:
[tex]v_a - v_w = 100[/tex]
[tex]v_a - 180 + v_a = 100[/tex]
[tex]2v_a = 280[/tex]
[tex]v_a = 140[/tex]
[tex]v_w = 180 - 140 = 40{/tex]
Hence:
- The rate of the plane in still air is of 140 mph.
- The rate of the wind is of 40 mph.
More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569
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