Multiple choice

An aeroplane leaves an airport and flies due north, at a speed of $1000km$ per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of $1200km$ per hour. How far apart will be the two planes after $1\cfrac{1}{2}$ hours?

  1. $300\sqrt {5}m$
  2. $300 m$
  3. $300\sqrt {61}m$
  4. $3000m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

After 1.5 hours, the north-bound plane travels 1000 * 1.5 = 1500 km, and the west-bound plane travels 1200 * 1.5 = 1800 km. The distance between them is the hypotenuse of a right triangle: sqrt(1500^2 + 1800^2) = sqrt(2250000 + 3240000) = sqrt(5490000) = 300 * sqrt(61) km. The unit in the options is listed as 'm' but should be 'km'.

AI explanation

Using the formula distance equals speed times time, in 1.5 hours the first plane flies 1500 km and the second plane flies 1800 km. Since the paths are perpendicular, use the Pythagorean theorem to find the distance between them: 1500 squared plus 1800 squared equals the square of the distance. This gives 2,250,000 plus 3,240,000 equals 5,490,000. The square root of 5,490,000 factors to 300 times the square root of 61 km.

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