Question 885722
RT=D for rate, time, distance.


10 mph = the speed of just the wind
Let r = the speed of the plane if no wind


DATA TABLE often helps to think clearly about all the values and numbers used in the problem description.



______________________speed_________time_________distance
WITH WIND_____________r+10__________(____)_______150
AGAINST Wind__________r-10_________(_____)_______150
TOTAL_______________________________3.75


You need expressions for times.  RT=D means you can divide left and right members of such an equation by R, so you have T=D/R.   Use this to fill the time slots in the table.


______________________speed_________time_________distance
WITH WIND_____________r+10__________{{{150/(r+10)}}}_______150
AGAINST Wind__________r-10_________{{{150/(r-10)}}}_______150
TOTAL_______________________________3.75



The time column including the total gives you an equation in the variable, r:
{{{highlight(150/(r+10)+150/(r-10)=3.75)}}}.
That is a large part of this solution process:  That analysis and obtaining the outlined equation.
Solve the equation for r.


(I used r, while you used s.  I hope you are not bothered by that.)
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(Now I see you got the same equation as I did, but you could not get an answer you were comfortable with.  Did you try multiplying left and right sides by (r+10)(r-10) and then simplify?)


Excuse me for skipping several steps; but you could get to 
{{{3.75^r^2-300r-375=0}}}, and since the mixed decimal involves a denominator of 4, you can multiply left and right members by 4, yielding
{{{15r^2-1200r-1500=0}}} and continue to simplify this

{{{highlight(highlight(r^2-80r-100=0))}}} ---- Now, solve THAT for r.
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Use the general solution of a quadratic formula and simplify your expression.  I found {{{highlight(r=50+10sqrt(17))}}}.