+448 A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 3 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 30 miles per hour, the trip takes 3 hours and 45 minutes. How many miles is the distance from Penthaven to Jackson?
(Assume that the plane flies at a constant speed, and that the turnaround time is negligible.)
+15001 How many miles is the distance from Penthaven to Jackson?
\(s=vt\\ 2s=v\cdot 3.6h\\ 3.75h= \frac{s}{v+w}+\frac{s}{v-w}\\ 7.5h=\frac{2s}{v+w}+\frac{2s}{v-w}=\frac{v\cdot 3.6h}{v+30miles/h}+\frac{v\cdot 3.6h}{v-30miles/h}\\ 7.5=\frac{3.6v}{v+30miles/h}+\frac{3.6v}{v-30miles/h}\\ \color{blue}v=150\ miles/h\)
\(2s=v\cdot 3.6h\\ s=\frac{v\cdot 3.6h}{2}=150miles/h\cdot1.6h\\ \color{blue}s=240\ miles\)
240 miles is the distance from Penthaven to Jackson.
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