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With a tail wind, a plane traveled 840 miles in 3hrs. With the same wind as a head wind, the return trip took 30 minutes longer. Find the plane's airspeed(in still air) and the wind speed....
So lost smh

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nathan127
Tail Wind: 840 miles in 3 hours (i.e. Plane is going with the wind)
Head Wind: 840 miles in 3.5 hours (i.e. Plane is going against the wind)

Let the plane speed (without wind) i.e. airspeed = v
Let the wind speed = w

The two equations can be made
1. v + w = 840 miles in 3 hours 
   v + w = 280 miles per hour
2. v - w = 840 miles in 3.5 hours
    v - w = 240 miles per hour

This is a set of simultaneous equations. We can either solve with substitution or elimination. I choose elimination

v + w = 280
- (v - w = 240)
2w = 40
w = 20
So the wind speed, w, is 20 miles per hour

We can then substitute w = 20 into either equation to find v.
v + w = 280 miles per hour
v + 20 = 280
v = 260

So the planes airspeed, v, is 260 miles per hour


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