Question 937771

A helicopter flew 15 miles against a 25 mph headwind.  Then it flew back with the wind at its tail.  The round trip lasted 27 minutes.  Find the helicopter's speed in still air.
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Let speed in still air be S
Then time taken to fly against the wind = {{{15/(S - 25)}}}
Time taken to fly with the wind = {{{15/(S + 25)}}}
Since total trip time was 27 minutes, or {{{27/60}}}, or {{{9/20}}} hr, then: {{{15/(S - 25) + 15/(S + 25) = 9/20}}}
15(20)(S + 25) + 15(20)(S – 25) = 9(S – 25)(S + 25) ----- Multiplying by LCD, 20(S – 25)(S + 25)
{{{300S + 7500 + 300S - 7500 = 9(S^2 - 625)}}}
{{{600S = 9S^2 - 5625}}}
{{{9S^2 - 600S - 5625 = 0}}}
{{{3(3S^2 - 200S - 1875) = 3(0)}}}
{{{3S^2 - 200S - 1875 = 0}}} 
(S – 75)(3S + 25) = 0
S, or speed in still air = {{{highlight_green(75)}}} mph	    OR		   S = {{{- 25/3}}} (ignore)