+452 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.)
+5 let the speed be x
time be in mins
so we can form an equation
which is 216x= 225(x-30)
if we expand, we get
216x=225x-6750
so 9x=6750
x=6750/9
=750.
Since the speed is 750 miles per min,
distance= 750*216=162000 miles (per min)
so we have to divide by 60.
162000/60=2700 miles per hour
+15054 How many miles is the distance from Penthaven to Jackson?
\(v_1=\dfrac{s}{t_1}=\dfrac{s}{108min}\\ t_2=\dfrac{s}{v_1+\dfrac{1mil}{2min}}+\dfrac{s}{v_1-\dfrac{1mil}{2min}}\\ 225min=\dfrac{s}{\dfrac{s}{108min}+\dfrac{1mil}{2min}}+\dfrac{s}{\dfrac{s}{108min}-\dfrac{1mil}{2min}}\\ 225min=\dfrac{s}{\dfrac{s+54mil}{108min}}+\dfrac{s}{\dfrac{s-54mil}{108min}}\)
\(225min=\dfrac{s\cdot 108min}{s+54mil}+\dfrac{s\cdot 108min}{s-54mil}\\ 225min(s^2-54^2mil^2)=s\cdot 108min(s-54mil+s+54mil)\\ s^2-54^2mil^2=\dfrac{216s^2}{225}\\0.04s^2=54^2mil^2\\ 0.2s=54mil\\ \color{blue}s=270\ mil\)
The distance from Penthaven to Jackson is 270 miles.
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