Togo Flew His Ultralight Plane To A Landing Field 30 Mi Away. With The Wind, The Flight Took 3/5 H. Returning Against The Wind, The Flight Took 5/6 H. Find The Rate Of The Plane In Still Air And The Rate Of The Wind?

The sum of the rates is (30 mi)/(3/5 hr) = 50 mph.
The difference of the rates is (30 mi)/(5/6 hr) = 36 mph.
The plane's speed is the average of these: (50 mph + 36 mph)/2 = 43 mph
The wind's speed is half the difference of these: (50 mph - 36 mph)/2 = 7 mph

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Suppose p is the speed of the plane and w is the speed of the wind.
  p + w = sum
  p - w = difference Add these two equations to get
  (p + w) + (p - w) = sum + difference
  2p = sum + difference
  p = (sum + difference)/2 Subtract the second equation from the first to get
  (p + w) - (p - w) = sum - difference
  2w = sum - difference
  w = (sum - difference)/2
It is useful to remember this solution to sum and difference problems, as you are likely to see a lot of algebra problems that can make use of it.