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

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