A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $5$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $8$ hours. How many miles is the distance from Penthaven to Jackson?

omgitsrne Jan 1, 2024

#1**+1 **

5 hrs 20 min = ( 5 + 1/3 ) hrs

Let the speed of the plane from Jackson to Penthaven = S

Let the speed of the plane form Penthaven to Jackson = S - 70

So

Rate * Time = Distance.......the dstance between the towns is equal.....so....

S (5 + 1/3) = (S - 70) (8)

5S + S/3 = 8S - 560

(16/3)S = 8S - 560

560 = 8S - (16/3)S

560 = (8/3)S

560 (3/8) = S

210 = S

Distance form Penthaven to Jackson = (S -70) (8) = (210 - 70) (8) = 1120 miles

CPhill Jan 2, 2024