Question

Las Cruces, NM, is about 600 mi from Dallas, TX. One plane flies from

Dallas to Las Cruces in 1 hr 12 min. and another plane with the same
air speed flies from Las Cruces to Dallas in 1 hr 30 min. Find the air
speed of the planes and the speed of the wind.

Answer 1

The air speed of the plane is 450 mph and that of the wind is 50 mph.

Explanation:

Let the speed of the plane is u and that of wind is v.

Therefore, with (u + v) speed the plane goes from Dallas to Las Cruces, i.e. 600 miles in 1 hr and 12 minutes i.e. 1.2 hours.

So,
`u + v = (600)/(1.2) =500` .......... (1)

And with (u - v) speed the plane goes from Las Cruces to Dallas in 1 hour and 30 minutes i.e. 1.5 hours.

So,
`u -v = (600)/(1.5) =400` ......... (2)

Solving equation (1) and equation (2), we get 2u = 900, ⇒ u = 450 miles per hour.

Now, from equation (1), we get, v = 500 - 450 = 50 miles per hour.

So, the airspeed of the plane is 450 mph and that of the wind is 50 mph. (Answer)