Multiple choice

An aeroplane travels $4362$ km against the wind in $6$ hours and $5322$ km with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?

  1. $807 \ km/hr$ and $80 \ km/hr$
  2. $800 \  km/hr$ and $12 \ km/hr$
  3. $600 \ km/hr$ and $ 50 \  km/hr$
  4. $300 \ km/hr$ and $ 25 \ km/hr$
  5. $ 200 \ km/hr$ and $ 20 \  km/hr$
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A Correct answer
Explanation

Let p be plane speed and w be wind speed. (p-w) = 4362/6 = 727. (p+w) = 5322/6 = 887. Adding equations: 2p = 1614 => p = 807. Subtracting: 2w = 160 => w = 80.

AI explanation

The rate of the plane against the wind is 4362 km / 6 hours = 727 km/hr, and the rate with the wind is 5322 km / 6 hours = 887 km/hr. The speed of the plane in still air is the average of these two speeds: (727 + 887) / 2 = 807 km/hr. The rate of the wind is half the difference between these two speeds: (887 - 727) / 2 = 80 km/hr.

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