Question 1025505
Time is distance over rate, t = d/r.  We will use r for the rate in still air.
The plane's first time is t = 500/(r+30).
The plane's second time is t = 350/(r-30).
These are equal times, so
{{{500/(r+30) = 350/(r-30)}}}
Now solve...
500(r-30) = 350(r+30)
500r - 15000 = 350r + 10500
150r = 25500
r = 170 mph