Answer:
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
