Question 1030170
The helicopter could fly at 4 times the speed of the wind. Thus, it could travel 600 miles downwind in 1 hour more than it took to travel 300 miles upwind. What was the speed of the helicopter in still air? 
---I am not sure how this problem is solved. I have done other problems somewhat similar to this, but this is a bit more difficult. An explanation would be greatly appreciated. Thank you!
<pre>Let the speed of the helicopter, in still air, be S
Then speed of wind = {{{matrix(1,3, (1/4)S, or, S/4)}}}
Time it took to travel downwind: {{{600/(S + S/4)}}}
Time it took to travel upwind: {{{300/(S - S/4)}}} 
We then get: {{{600/(S + S/4) = 300/(S - S/4) + 1}}}
{{{600(S - S/4) = 300(S + S/4) + 1(S + S/4)(S - S/4)}}} ----- Multiplying by LCD, {{{(S + S/4)(S - S/4)}}}
{{{600S - 150S = 300S + 75S + S^2 - S^2/16}}}
{{{450S = 375S + S^2 - S^2/16}}} 
{{{S^2 - S^2/16 + 375S - 450S = 0}}}
{{{S^2 - S^2/16 - 75S = 0}}}
{{{16S^2 - S^2 - 16(75S) = 0}}} ------- Multiplying by LCD, 16
{{{15S^2 - 16(75S) = 0}}}
{{{15(S^2) - 15(5S)(16) = 0}}}
{{{S^2 - 80S = 0}}}
S(S - 80) = 0
S or speed or helicopter, in still air = {{{highlight_green(matrix(1,2, 80, mph))}}}	   OR	      S = 0 (ignore)