It took a plane 2 hours to go from Dallas to NY with the head wind and 1.5 hours to get back with the tail wind. If the speed of the wind was 30 mph, how far apart are two cities?

360 miles

Step-by-step explanation:

let speed of plane be x

speed of wind be c

Also note D = RT, where

D is distance and R is rate and T is time

For First Leg:

we can write:

(x - c) * 2 = D

2x - 2c = D

For Second Leg:

we can write:

(x+c) * 1.5 = D

1.5x + 1.5c = D

We can equate and write:

2x - 2c = 1.5x + 1.5c

0.5x = 3.5c

We know Speed of Wind, c, is 30, so we have:

0.5x = 3.5 (30)

0.5x = 105

x = 105/0.5 = 210 [speed of airplane]

We know distance is

D = 2x - 2c

D = 2 (210) - 2 (30)

D = 420 - 60

D = 360 miles

The distance is 360 miles