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
