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AfilCa [17]
3 years ago
8

In 1 hr, a plane can travel 390 mi into the wind and 470 mi with the wind. Find the wind speed and the rate of the plane in stil

l air.
The wind speed is mph.
The rate of the plane in still air
mph
Mathematics
1 answer:
Komok [63]3 years ago
7 0

Let <em>w</em> be the wind speed and <em>p</em> the plane's speed in still air.

Flying against the wind, the plane has velocity

<em>p</em> - <em>w</em> = 390 mi/h

and flying with it, it has

<em>p</em> + <em>w</em> = 470 mi/h

Add the two equations together to eliminate <em>w</em> and solve for <em>p</em> :

(<em>p</em> - <em>w</em>) + (<em>p</em> + <em>w</em>) = 390 mi/h + 470 mi/h

2<em>p</em> = 860 mi/h

<em>p</em> = 430 mi/h

Subtract them to eliminate <em>p</em> and solve for <em>w</em> :

(<em>p</em> - <em>w</em>) - (<em>p</em> + <em>w</em>) = 390 mi/h - 470 mi/h

-2<em>w</em> = -80 mi/h

<em>w</em> = 40 mi/h

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