A plane flies from Springville to Brockton and then back to Springville. When there is no wind, the round trip takes 6 hours and 24 minutes, but when there is a wind blowing from Springville to Brockton at 50 miles per hour, the trip takes 6 hours and 40 minutes. How many miles is the distance from Springville to Brockton?

Step-by-step explanation:

Let x represent the speed of the plane in still air.

When there is no wind, the round trip takes 6 hours and 24 minutes. Converting to hours, it becomes

6 + 24/60 = 6 + 0.4 = 6.4 hours

Distance = speed * time

Distance of the round trip = 6.4x

But when there is a wind blowing from Springville to Brockton at 50 miles per hour, the trip takes 6 hours and 40 minutes. Converting 6 hours and 40 minutes, it becomes

6 + 40/60 = 6 2/3 = 20/3 hours

The total speed would be

(x - 50) miles per hour

Distance covered = 20/3 (x - 50)

Therefore, since both round trips are the same distance, then,

6.4x = 20/3 (x - 50)

Cross multiplying by 3, it becomes

19.2x = 20 (x - 50)

19.2x = 20x - 1000

20x - 19.2x = 1000

0.8x = 1000

x = 1000/0.8 = 1250 mph

Distance covered on the round trip is

6.4x = 6 * 1250 = 7500 miles

Therefore, the distance from Springville to Brockton is

7500/2 = 3750 miles